David Ortiz socked a pair of solo home runs and Jacoby Ellsbury went 3-for-4 to pace Boston.
Ellsbury scored three runs for the Red Sox, including their first, reaching on a single to right in the bottom of the first, stealing second and taking third when Rays' catcher, Jose Molina threw the ball errantly into center field. Ellsbury, who led the AL in steals with 52 during the regular season, scored on Dustin Pedroia's sac fly. The next batter, Ortiz, made it 2-0, staking starter John Lackey to a quick lead.
In the third, Ellsbury doubled in a run and scored again, this time on a ground out fielder's choice by Pedroia. Ellsbury scored again in the fifth, when he singled and raced around from first on a double to left by Pedroia.
It was the first time Ortiz had gone yard twice in a post-season game.
The Red Sox will be looking for the sweep and advancing to the ALCS when they play the Rays in game three at Tropicana Field, Monday at 6:07 pm EDT.
In Oakland, the A's got a run in the bottom of the ninth when Stephen Vogt singled with the bases loaded to score Yoenis Cespedes with the only run of the game and a 1-0 win for the Oakland A's.
Starters Justin Verlander and Sonny Gray engaged in an old-fashioned pitcher's duel through much of the game. Verlander allowed just four hits and fanned 11, lasting seven innings. Gray also allowed four hits and fanned nine, working through eight innings. A's closer, Grant Balfour, took the win, getting the Tigers out in order in the top of the ninth.
The series, now tied, 1-1, moves to detroit on Monday for game three, at 1:07 pm EDT.
There were no National league games on Saturday. Both divisional series are tied at a game apiece and resume on Sunday. The Cardinals visit the Pirates at 4:37 pm EDT and the Braves play the Dodgers in LA at 8:07 pm EDT.
Today's Trivia: Who stole more bases during their major league career, Mickey mantle or Willie Mays? (answer tomorrow)
Yesterday's Answer: Tom Seaver and Tommy Agee were the two former rookies of the year that played on the World Champion NT Mets of 1969. Seaver won the award in 1967 as a Met, Agee was AL ROY in 1966, playing for the Chicago White Sox.