After Jarrod Saltalamacchia flew out to deep center field, Ellsbury -- who smacked two solo shots in the day's first game -- unloaded on a 1-0 pitch and sent it into the Yankees bullpen for a three-run shot.
The Game 2 victory enabled the reeling Red Sox to hang onto a half-game lead over Tampa Bay atop the American League wild card standings after losing the first contest 6-2.
Franklin Morales (1-1) earned the victory with two scoreless innings and Felix Doubront collected the save with a 1-2-3 bottom of the 14th for the Red Sox, who improved to just 6-18 in September.
Boston now heads to Baltimore for three games to end the season, while the Rays host the Yankees.
The Los Angeles Angels also remained alive in the wild card, three games behind the Red Sox. They will host AL West champion Texas.