The Rays had taken a 4-3 lead in the eighth on a run-producing groundout from Delmon Young, but the Red Sox responded in the top of the ninth on Dustin Pedroia's two-out, bases-loaded grounder against Fernando Rodney (1-0).
In the ninth, Red Sox closer Koji Uehara (0-1) retired the first two Rays batters, but Lobaton then bashed a pitch deep over the right-centerfield fence and into the Tropicana Field ray aquarium.
Evan Longoria belted a score-tying, three-homer in the fifth for Tampa Bay, which avoided elimination in their American League division series and forced a Game 4, set for Tuesday in St. Petersburg.
Beautician charged with giving client fatal silicone butt injection
Duggar sisters unveil Christian dating rules in new book