Dangerously close to getting swept, the New York 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.

“I don’t think we’re ready to see Roger Clemens’ last steps off the mound, or Joe Torre’s last game,” Damon said. “We have a lot to play for.”

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 former-Yankee 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 and 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.

“We know what we have to do. We know who’s the boss around here, and we know how much we love Joe Torre,” Damon said. “We battled, we got some big hits, and a big pitching performance from Philip Hughes.”

In a game that mirrored the Yankees’ comeback from a 21-29 start, Cano added a bases-loaded RBI single in the sixth off Aaron Fultz. 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 2-3 innings of one-run relief.

“This is a very uncomfortable time of year. It’s an exciting time of year,” Torre said. “You understand there’s no safety net.”

In an unprecedented year of the sweep, all other division series ended in three-game wipeouts. But the Indians, at least for a night, were denied their first trip to the AL championship series since 1998.