Jackson (7-4) gave up only a solo homer to Ryan Garko in the fifth, in helping the Tigers win their third straight. He was given a 3-0 lead in the second when Gerald Laird delivered an RBI double and Josh Anderson had a two-run single.
The other Detroit runs came on the one-out homer by Thames in the eighth after Placido Polanco had drawn a four-pitch, leadoff walk.
Cliff Lee (4-9) allowed three runs over seven innings to lose his third straight start. Cleveland went 0-for-9 with runners in scoring position.
Detroit has won six of its seven meetings with the Indians this year.