The White Sox fell six games behind idle Minnesota in the AL Central, their largest deficit since June 17.
Detroit has won six of eight to get back above .500 for the first time since July 31.
Gavin Floyd (10-12) allowed six runs over six innings. He gave up 13 hits, all of which were singles.
Chicago's Alex Rios hit a two-run homer in the fourth.
The Tigers didn't hit one over the fence, or even in a gap, but methodically found holes to score twice in the first, two more in the third, one in the fourth and a sixth run in the seventh inning.
Damon had his first of four hits in the first as Detroit took a 2-0 lead.
Ryan Raburn and Jhonny Peralta each had two RBIs as the Tigers won for the ninth time in 10 games at Comerica Park, where they are 46-26. The Tigers trail the Twins by 12½ games in large part because they're 19 games under .500 on the road.
Notes: Chicago activated reliever J.J. Putz from the disabled list before the game. ... The Tigers were without slugger Miguel Cabrera (left shoulder, biceps) for a second game in a row. ... Chicago is 28-32 against AL Central teams, Detroit is .500 in the division and the Twins are 38-19 against the White Sox, Tigers, Royals and Indians. ... Tigers RHP Armando Galarraga says it will be "no big deal" to pitch for the first time since his near-perfect game with umpire Jim Joyce on the field Friday night against Baltimore.