The AL West-leading Rangers are 5-1 since the All-Star break.
Hunter became the first Ranger to start a season 7-0, pitching only as a starter. He gave up three hits and two walks.
Detroit has lost a season-high seven straight, following a trend during the Jim Leyland era. The Tigers have had at least a .500 record before the break in each of Leyland's five seasons and haven't had a winning record once after it.
Armando Galarraga (3-3) gave up four runs and nine hits over 7 1-3 innings.
Elvis Andrus hit Galarraga's first pitch for a single, scored on Kinsler's triple and Josh Hamilton followed with a sacrifice fly. David Murphy's solo homer in the second put Texas up 3-0.
Nelson Cruz's RBI single in the sixth brought Hamilton home, providing the Rangers with more than enough offense.
But the Rangers stayed aggressive and turned the game into a rout with a four-run ninth against relievers Brad Thomas and Casey Fien, who was recalled earlier in the day from Triple-A Toledo to take Brandon Inge's spot on the roster.
Andrus' suicide squeeze gave Texas a five-run cushion in the final inning, Kinsler's two-run homer and Hamilton's solo shot made it 8-0.
Detroit didn't have a hit off Hunter until Austin Jackson led off the fourth with a single.
The Tigers looked like they might score in the seventh, but a slick play in the field prevented them from doing that. Miguel Cabrera hit a one-out double and Brennan Boesch walked on four pitches. Ryan Raburn followed with a sharply hit grounder in the hole between third and second, Andrus dove to stop it and made a throw from his right knee to stunt the potential rally.
NOTES: Texas' Dustin Nippert says he didn't sustain any significant injuries when he was hit by a batted ball during Monday night's game against Detroit. ... The Rangers, who had lost 11 straight at Detroit before winning in 14 innings on Monday night, have won a series at Comerica Park for the first time since 2007 and they can go for a sweep on Wednesday. ... Detroit has lost seven in a row for the first time since the start of the 2008 season. ... The Tigers put Inge on the 15-day DL with a broken left hand and replaced him in the field with Don Kelly, who dove to stop two grounders and made throws on both plays to get outs.