The Red Sox got an RBI single from Dustin Pedroia with two outs in the top of the 16th inning to top the Rays 1-0 on Sunday night.
Josh Beckett and five relievers combined to pitch a three-hitter for the Red Sox, who won for the eighth time in nine games.
"I just wanted to go home. I think everybody did," Pedroia said.
"They threw the ball outstanding all night and we did, too. It was a great game. I'm just happy we won."
It was the longest 1-0 game in the major leagues since the Brewers at Angels on June 8, 2004, went 17 innings.
Red Sox Top Rays 1-0 In 16 Innings