Donovan's reputation as the pin-up boy of U.S. soccer was reinforced as he touched home the ball in the 91st minute after setting up the attacking move that culminated in the winner.
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It moved the Americans from the brink of elimination at the first stage of a second successive World Cup finals to the top of Group C.
Wave after wave of attack in the closing stages made for a frantic finish and Pretoria's Loftus Versfeld, packed with large contingents of U.S. and Algerian supporters, erupted into near pandemonium when the Algerian goal was finally breached.
Donovan, who broke down in tears at the post-match press conference afterwards, provided the finishing touch to a move he started in midfield when time seemed to be running out for his side.
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He passed right to Jozy Altidore, who hit a square ball into the penalty area where Clint Dempsey's effort was smothered by Algerian goalkeeper Rais Ouhed Mbouli, only for Donovan to snatch up the loose ball and score.
DONOVAN BREAKS DOWN
"Sometimes you have games like this when you have a lot of chances and they don't go in. The only thing you can do is to keep going," said Donovan before breaking down after a question about the emotions he felt as the winner hit the net.
"I've been through a lot in the last four years," he said in a reference to the criticism he received after the United States were eliminated early at the last World Cup and his divorce last year from his actress wife.
Coach Bob Bradley praised the attacking enterprise of both teams but reserved effusive praise for the Americans fans. "It is not often you see them lining up on the road before the game, all dressed up and chanting and banging on the bus," he said.
"That was a really special moment for the team."
Both sides rattled the woodwork during the game but the Americans proved more enterprising, their physical conditioning showing as they kept up a relentless tempo, even increasing their effort as their World Cup hopes looked to be slipping away.
Dempsey and Donovan combined for several near efforts, the best of which came in the 57th minute when Dempsey hit the woodwork and then botched the rebound.
He also had an opportunity midway through the first half ruled offside and was denied twice by Mbouli.
Donovan skewed wide a glaring chance right in front of goal seven minutes from half time after persistent play from Michael Bradley set him up with the goal yawning in front of him.
Bradley was again the driving force for the Americans, who dominated the midfield.
Algeria are the fourth African side eliminated, going home without scoring. They
