Tampa Bay took a win-or-go-home game for the fourth time in nine days. The Rays did it with an unlikely stroke as Lobaton, who came off the bench late in the game, connected against Red Sox closer Koji Uehara.
"It's unbelievable. It's something you can't explain," Lobaton said. "We never give up. We're going to keep fighting."
Back home after two weeks on the road, the Rays gave a sellout crowd of 33,675 little to cheer until Evan Longoria homered on his 28th birthday. Longoria's three-run shot off Clay Buchholz with two outs in the fifth rallied Tampa Bay to a 3-all tie. Longoria's homer was his ninth in 109 career postseason at-bats.
Pinch-hitter Delmon Young, who has a penchant for driving home key runs in October, put the Rays ahead 4-3 with an RBI grounder in the eighth.
The Red Sox tied it in the ninth against Rays closer Fernando Rodney. Dustin Pedroia's RBI grounder made it 4-all.
Rodney got the win when Lobaton homered to right-center, into the 10,000-gallon tank where cownose rays swim around.
Uehara did not give up a home run in his final 37 regular-season appearances.
The Rays won three must-win road games in three cities over four days just to get into the division series, so they felt good about their chances of coming back against the Red Sox.