Ben Zobrist hit a tie-breaking solo run blast in the eighth card lead with a 6-2 win over Toronto on Saturday.
The Rays bounced back from a 5-1 loss in the opener of this three-game series on Friday and will try to inch even closer to Boston in Sunday's finale.
Alexander Torres (1-1) earned the win for Tampa Bay, throwing five scoreless innings after taking over for ailing starter Jeff Niemann in the second.
Zobrist knocked Romero's 2-1 fastball over the wall in left-center leading off the fourth inning, giving the Rays a 3-2 lead with his 18th homer of the season.
Romero was taken out after Damon's three-run blast in the eighth. The left- hander gave up six hits, two walks and struck out five.
Damon had three hits and four RBI in the game. His 16th homer of the season cleared the wall in right field, scoring B.J. Upton and Evan Longoria for Tampa Bay's four-run cushion.
Niemann labored through the first inning, possibly because of a sore back that pushed his scheduled start back two days. The right-hander threw 38 pitches in his only inning of work, giving up two hits and two walks.
One of the hits was Bautista's major league-leading 43rd homer, a line-drive blast over the left field wall that also scored Eric Thames.
Niemann worked out of further trouble in the first, stranding runners at second and third base, and Tampa Bay tied the game in the bottom of the inning.
Upton hit a one-out single, stole second base and scored when shortstop Mike McCoy bounced a throw past first on Zobrist's grounder. Damon followed with a double, scoring Zobrist from second for the 2-2 tie.
After Zobrist's homer in the fourth, Damon walked and moved to second base on a ground out. The inning ended when Romero deflected Matt Joyce's sharp liner and McCoy raced in front of second base to pick it up, gunning the runner down by a step.
Niemann failed to earn a decision for the first time since July 23, a span of 11 starts...Toronto went 0-for-2 with runners in scoring position and stranded six men on base, while the Rays were 2-for-10 and left three runners on...Romero was 8-1 in his previous 11 starts.