Game 5 is Thursday night in Detroit. The Tigers' Anibal Sanchez faces Boston's Jon Lester in a rematch of Game 1, which was won by Detroit 1-0.
Jacoby Ellsbury had four hits for the Red Sox, finishing a homer shy of the cycle.
The Tigers lost Games 2 and 3, wasting gems by Max Scherzer and Justin Verlander. Jackson was 3 for 33 with 18 strikeouts in the postseason before Wednesday, and although Leyland left him in the lineup, he changed the batting order. Jackson hit eighth, and with others moving up a spot, it made for an odd-looking order. Hunter hit leadoff for the first time since 1999 and Cabrera was second for only the third time in his career first since 2004.
Jackson found himself batting in a crucial situation right away, with the bases loaded and one out in the second. Peavy walked him on four pitches to force home the game's first run.
The Red Sox had a chance to halt that rally when Jose Iglesias hit a potential double play grounder to second, but Dustin Pedroia couldn't field it cleanly and Boston had to settle for a forceout at second that brought another run home.
Hunter followed with a double down the line in left to make it 4-0, and Cabrera added an RBI single.
After walking three batters in the second inning, Peavy was in trouble again in the fourth. After a leadoff double by Omar Infante, Jackson slapped a single past a diving Pedroia to bring home a run.
Cabrera's single made it 7-0, and the Detroit third baseman who has been running even slower than usual over the last month or so because of groin problems caught reliever Brandon Workman and the Boston defense napping when he stole second without a throw.
In the fifth, Cabrera looked healthy enough when he charged Pedroia's slow grounder, barehanded it and threw to first for the out.
Peavy allowed seven runs and five hits in three-plus innings.