Lester (1-0) gave up two home runs but there was just one other Tampa Bay hit through his 7 2/3-inning outing. He retired 12 of the last 14 batters he faced.
He walked three -- two in the eighth -- and struck out seven.
The win gave Boston a 1-0 lead in the best-of-five American League Division Series. Game 2 is set for 5:30 p.m. EDT Saturday in Boston.
It was the first loss for Tampa Bay since Sept. 28 as the Rays won three elimination games -- the final game of the regular season, the tiebreaker with the Texas Rangers and the AL wild-card game at Cleveland.
The streak seemed to go on early in Friday's game with home runs by Sean Rodriguez in the second inning and Ben Zobrist in the fourth putting the Rays up 2-0. But the Red Sox batted around in both the fourth and fifth innings, scoring eight runs, all of which were charged to Tampa Bay starter Matt Moore (0-1).
The Boston five-run fourth started with a Dustin Pedroia single. David Ortiz hit a fly that Rays right fielder Wil Myers misplayed into a ground-rule double. After an out, Jonny Gomes tied the score by banging a double off the left-field wall.
Moore got a strikeout but Stephen Drew singled in Gomes and Will Middlebrooks doubled in Drew. Moore got another strikeout but Jacoby Ellsbury reached on a passed ball on the play, keeping the inning alive.
Victorino had an RBI single giving him three hits in the game, and scored on a based-loaded walk in the eighth. Another run scored on a double play and Saltalamacchia capped the rout with a run-scoring single.