Jose Valverde, who was 49-for-49 in save opportunities a year ago, gave up a leadoff double to Dustin Pedroia to start the ninth.
"We've got a great group of guys," said Pedroia. "We're going to fight for 162 games, that's for sure. We saw the best pitcher in baseball. He threw the ball well and we fought there at the end."
Adrian Gonzalez followed Pedroia by lining an opposite-field single to left, and David Ortiz lined a sacrifice fly to center to bring his team within a run.
Darnell McDonald came off the bench to run for Gonzalez and promptly stole second.
With the tying run now in scoring position, Valverde suddenly had a lot more on his mind. And Ryan Sweeney, making his debut with the Sox, became the hero, lacing a game-tying triple off the wall in right.
"He fell behind 2-0 and threw me an elevated fastball and threw me a split-finger down and in, and I put a good swing on it," Sweeney said. "I thought I got it at first when I hit it, but it just hit off the wall and it got away from him and I made it to third."
Cody Ross lined to short to end the threat, and Boston's bullpen succumbed in the bottom of the ninth.
But the comeback was not lost on the players, who are trying to erase memories of last September's epic collapse.
"Like I told everyone after the game, 'Come back on Saturday and play.' Actually I said Friday," Ortiz said. "I said Friday [an off-day] but somebody tells me, 'You're going to be all by yourself tomorrow.' There's adrenaline going on, but that's how it is. You can't look back. You have to come back with the same attitude and keep on playing. It was a good game."
Ian Browne is a reporter for MLB.com. Read his blog, Brownie Points, and follow him on Twitter @IanMBrowne. This story was not subject to the approval of Major League Baseball or its clubs.