BOSTON—Down seven runs and running out of time, the Boston Red Sox weren’t quite ready to go away.

The defending World Series champions pulled off the major leagues’ biggest postseason comeback in 79 years, beating the Rays 8-7 Thursday night on J.D. Drew’s two-out single in the ninth to stave off elimination in the AL championship series and head to Tampa Bay trailing three games to two.

With the score 7-all, Kevin Youkilis grounded to Evan Longoria with two outs, and wound up at second when the throw bounced in front of first baseman Carlos Pena. Youkilis was given an...

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