There were various man-bites-dog scenarios, each more fantastical than the next, that had the United States national soccer team shaking off two comprehensive defeats and somehow earning a berth today in the Confederations Cup semifinals.

To give you an idea of how extraordinary the scenarios were, this was the least ridiculous: U.S. 3, Egypt 0 … Brazil 3, Italy 0.

And that was exactly what happened. Yielding a three-way tie for second in Group B between the U.S., Italy and Egypt, and the Americans advancing on the basis of goal differential (over Egypt) and goals scored (over Italy).

And now the Americans can savor one of their best international victories … before getting Spain, ranked No. 1 in the world, in the Confederations Cup semifinals on Wednesday.

This was a fairly amazing turn of events.

First, a disclaimer. As well as the Americans played, as plucky as the Yanks were, as determined in the attack and dogged in defense … it doesn’t vault them into the world’s elite. The matches against Italy and Brazil indicated otherwise. Just as the match on Wednesday against Spain — which will be looking to set world soccer records with its 16th consecutive victory as well as 36th consecutive unbeaten match — isn’t quite a fair test for the U.S., either.

But for a day, this was as pleasant an international soccer surprise as U.S. fans have experienced … perhaps since the 3-2 upset of Portugal to open the 2002 World Cup. Or the1-0 Gold Cup final upset of Brazil in 1998. Or perhaps even the 1-0 victory in Port of Spain, Trinidad, that put the Americans into the 1990 World Cup — and on the world soccer map.

(Look for video highlights of the match here, at FIFA.com; the video is down the page, on the right side. Or here, at ESPN.com, which doesn’t include the final goal, for whatever reason.)

This was a victory for American spirit, because many teams would have shown up disheartened and disinterested after  losing 3-1 to Italy and 3-0 to Brazil.  “Let’s put in the 90 minutes, go back to the hotel to pack and be back stateside on Monday.”

But the U.S. took the initiative from the first minute, dominated play for 70 minutes, showed imagination and flair and even some finishing skill (with all three goals coming in the run of play), and then hung on grimly over the final 20 minutes to secure the improbable meeting with Spain. (As well as, presumably, a third-place match against South Africa next Saturday.)

Perhaps most critical to this match, aside from Yankee grit, was the opposition.

Egypt arrived seeming distracted or bored or perhaps entitled and fat-headed from the plaudits that came after its narrow, 4-3 defeat to Brazil and its 1-0 victory over Italy. The Americans would be easy, right?

Turns out, Egypt is competent but not remotely as physically gifted as Brazil or as tactically clever as the Italians. (Not did it help that Egypt’s most interesting forward,  Zidan, sat out the match with an injury.)

The Americans had time to hold the ball, look around, and out-run the Egyptians. None of that happened more than once or twice against Brazil and Italy.

Landon Donovan was particularly effective, though he didn’t add to his U.S.  record goal total of 40. Playing at outside midfield, in his third match in seven days, he tracked back doggedly on defense and pushed ahead relentlessly. He seemed to put the Egyptians on their heels with some of his early runs, including one in which he weaved through half the Egyptian side before finally being stopped in the box by the keeper. It was the sort of run, a combination of dribbling and speed, that no other American currently is capable of pulling off. The kind of run that would have left him dispossessed early, against Brazil and Italy. But was doable against the Egyptians.

Not giving up the early goal helped. The first goal helped even more, a rather lucky affair that ended with Charlie Davies standing nearly on the end line as he knocked a ball off the prone Egyptian goalie’s arm and into the net.

No doubt, the hard-working Yanks received additional inspiration at the half, when they learned that Brazil was ahead of Italy by, yes, that 3-0 score that gave them a shred of daylight to peer forward and imagine a semifinal with Spain.

They continued to come forward, as Egypt sat back more than a little, apparently ready to lose as long as it won the tiebreaker for second place — which would be their reward if they lost even 2-0.

The U.S. got the second goal on a precise and impressive series of passes between Donovan and Michael Bradley.

Donovan controlled a ball near the center circle, knocked it back to the advancing Bradley, and the two of them headed for the goal,  Donovan on the left, Bradley in the middle, half the Egyptian team ahead of them. About 25 yards out, Bradley fed the ball left to Donovan, who carried it about halfway through the far edge of the box, luring defenders (and the keeper) toward him … before he centered it right in front of Bradley, who was about 5 yards back upfield.

Bradley redirected the pass with his right foot, barely 10 yards from the goal, putting it into the far corner, beyond the reach of the diving goalie.

And now the Yanks could taste the improbable. One more goal, and if Brazil could keep Italy down …

In the 69th minute, U.S. coach Bob Bradley made an inspired substitution. Like everyone else watching the match, Bradley noticed that Clint Dempsey, nominally the right winger, was getting forward just fine but not getting back much. At all. (Wouldn’t want to trouble the great Premiership mid with all that running.) Bradley solved Dempsey’s defensive lapses by substituting midfielder Benny Feilhaber for forward Jozy Altidore, allowing Dempsey to move into the forward slot he already was drifting toward all day.

It paid off in a matter of two minutes.  Jonathan Spector stood alone over a ball about 30 yards out on the right side (Egypt wasn’t much defending anyone, by then), and he lofted a perfect ball toward the far post, where Dempsey ran onto it and headed it into the left side of the goal.

Three-nil, and holy mackerel.

It wasn’t quite a just goal, as these things go, because Dempsey had been little short of awful for 70 minutes, alternately, lazy, theatrical, meandering and selfish. ESPN commentator John Harkes called for him to be replaced. But Dempsey was in the box when the U.S. needed one more goal, and his finish was quite nice, we must concede.

Then came 20-some minutes of high anxiety, as Egypt managed to create some scoring chances against the Americans, who were 1) tired and 2) probably wondering nonstop about the score of the Brazil-Italy match.

Finally, it was over, and Bob Bradley looked as if he had had the weight of unemployment lifted off his shoulders, and the U.S. players celebrated like they had clinched a World Cup berth.

Several players had very strong games.

–Donovan proved himself worthy of the captain’s armband, turning in his third straight game remarkable for his work rate. If any player in the Confederations Cup ran more miles than he did in group play, I’d like to know about it. He also ran at Egypt, alarming its back line, and made the exquisite extra pass to Michael Bradley for the easy-as-pie finish on the second goal.

–Oguchi Onyewu was a rock in the middle of the defense that the Egyptian attack repeatedly was dashed upon. He seemed to win every ball in the air in the box.

–Jonathan Spector got forward repeatedly in a tireless performance at right back, and he served up the ball that Dempsey finished.

Michael Bradley and Ricardo Clark were effective in the middle of the park, and Jay DeMerit seemed to grow into his role next to Onyewu in the middle of the defense.

Anyway, yes, it was the most comprehensive victory by the U.S. over a team that was playing for something … in a very long time. At kickoff, you probably couldn’t have found 100 people in South Africa who thought the Americans would win, let alone win 3-0.

And now, this has turned out about as well as it could, for the Yanks. They never were going to beat Italy or Brazil (or it was massively unlikely), but they didn’t go to pieces, rallying to crush Egypt a step short of what would have been one of the highlights of Egyptian soccer history.

Now, it’s the U.S. that gets to measure itself against the best team on the planet, and then gets one more match, in the third-place game, where it presumably can run out Freddy Adu and Heath Pearce,  Danny Califf and Marvell Wynne and the lads who have been in South Africa for two weeks now without seeing a minute on the pitch.

Have to wonder how much the U.S. First XI has left in the tank. Donovan, Onyewu,  DeMerit, Beasley, Spector, Bornstein and Bradley have never left the field, playing something like 290 minutes in three matches over seven days. The Wednesday match will be their fourth in 10 days, which is just brutal.

Spain will have had an extra day to rest, on top of giving its regulars some breaks during its parade through the feeble Group A.

The goals for the Yanks, of course, will be to keep it close, keep organized in the back, see if they can get forward a bit — and try not to lose someone to a red card. It definitely helps to play an 11-man game with all 11 men.

It should be interesting, anyway. The Yanks and the Spaniards, a bit before noon (PDT) on Wednesday. A match we certainly didn’t see coming but absolutely look forward to.