Dangerously close to getting swept, the Yankees woke up just in time to save their season and perhaps Joe Torre’s job.

Johnny Damon lofted a go-ahead, three-run homer in the fifth inning, rookies Phil Hughes and Joba Chamberlain rescued Roger Clemens and the Yankees rallied past Cleveland 8-4 Sunday night, closing within 2-1 in their first-round AL playoff series.

Yankees owner George Steinbrenner blustered Saturday that Torre’s run as manager was in jeopardy of ending after 12 seasons — all concluding with postseason appearances. “I don’t think we’d take him back if we don’t win this series,” he told The Record of New Jersey.

And it looked grim for Torre and the Yankees when the Indians chased an injured Clemens in the third inning, building a 3-0 lead as Trot Nixon homered, and Ryan Garko and Jhonny Peralta drove in runs. Damon had three hits, drove in four runs and started the comeback with an RBI single in the third off Jake Westbrook. New York, which hadn’t gotten back-to-back hits in the series, then got three straight opposite-field hits from Hideki Matsui, Robinson Cano and Melky Cabrera for a run in the fifth.

Damon worked the count to 2-0 against Westbrook, then hit the ball on a high arc to right. As it cleared the wall to put the Yankees ahead 5-3, Cano raised both hands in the air down the third-base line and jumped twice. Damon went into a trot, and the crowd of 56,358 leapt with him.

Cano added a bases-loaded RBI single in the sixth off Aaron Fultz, and when a charging Nixon overran the ball in right field for an error, two more runs scored.

This time, there were no bugs to distract Chamberlain, who brought in his 100 mph heat. Bothered by swarms of flying insects at Cleveland in Game 2, he combined with Hughes and Mariano Rivera on 6.2 innings of one-run relief. In an unprecedented year of the sweep, all other division series ended in three-game wipe-outs.

But the Indians, at least for a night, were denied a trip to the AL championship series for the first time since 1998. Paul Byrd tries to close it out Monday night for the Indians, with Game 1 loser Chien-Ming Wang likely to come back on three days’ rest for the Yankees. Only four teams have overcome 2-0 deficits in the first round since the playoffs expanded in 1995.

With former New York City mayor and current presidential candidate Rudy Giuliani leading the cheering from his front-row seats, Alex Rodriguez stopped his postseason hitless streak at 18 at-bats with a second-inning single and also beat out an infield single. But he remained in a 6-for-54 (.111) playoff funk with no RBIs dating to his Game 4 home run against Boston three years ago.

New York, which led the major leagues in scoring with its highest total since 1937, pushed across just four runs — three on solo homers — in the first two games and batted .121.

While the Yankees got the lead-off man on in each of the first three innings, Derek Jeter bounced into double plays in the first and the third, and Jorge Posada hit into one in the second. Jeter also made a bad throw that led to the Indians’ first run.

Clemens, in his 24th and maybe final season, tried to pitch with an injured hamstring that limited him to one start in the past month. He never looked comfortable, falling behind nine of 13 batters. By the time Torre went to the mound to remove him with no outs in the third, Cleveland had taken a 1-0 lead on Garko’s RBI single in the first and Nixon’s home run in the second, which appeared to glance off the top of the right-field wall. Rodriguez came over to the mound and tapped the misfiring Rocket on his chest with his glove. Clemens, glove dangling from right hand, slowly walked to the dugout, down the steps and up the corridor to the clubhouse. It took him 59 pitches to get just seven outs.

New York, which overcame a 21-29 start to win the AL wild card, had turned to Clemens earlier this year, bringing the seven-time Cy Young Award winner out of retirement with a contract that paid him $17.4 million over the season’s final four months.