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.
Mena Suvari shares her delightfully awkward Christmas card photo
Video of Victoria’s Secret models trying to 'twerk' hits Instagram