The loss snapped the D-backs' three-game winning streak, preventing them from winning four in a row for the first time this season.
After looking good in his first two outings for the D-backs -- aside from that Buster Posey grand slam on July 13 -- left-hander Vidal Nuno did not have his good stuff on Monday and it was a struggle for him from the beginning.
"His pitches were up," D-backs manager Kirk Gibson said. "He didn't really have much crispness on the corners."
The first-place Tigers took a 2-0 lead in the second off Nuno.
Victor Martinez led off the inning with a walk and Torii Hunter hit an 88-mph fastball over the bullpen in left for his 14 homer of the year.
The Tigers added a run in the third when Austin Jackson homered to lead off the inning.
"It was his hot zone there and I just left it up," Nuno said of the Hunter home run. "The consistency wasn't there and he took advantage of it. Jackson, it was just a cutter that just came in and he just took advantage of it."
Meanwhile, Verlander seemed on top of his game early on as he held the D-backs hitless through three innings.
Aaron Hill singled to lead off the fourth and Paul Goldschmidt doubled to put runners on second and third. After a Miguel Montero groundout brought home Hill, Mark Trumbo lined a single to left to score Goldschmidt and pull Arizona to within a run.
"He came up against good hitters," Tigers manager Brad Ausmus said. "Left the ball a little bit up to Hill, Goldschmidt hit a ball on the inner part of the plate. So he wasn't location quite like he was the first few innings, but he got back to where he should."
Gerardo Parra tied the game at 3 when he hit a two-out home run to right in the sixth.
It wouldn't remain deadlocked for long, though, as Jackson led off the seventh with a sinking line drive to center that a sliding David Peralta could not come up with and Jackson was credited with a double.
One out later, Miguel Cabrera hit a drive to center that hit off the overhang below the yellow line.
Cabrera, thinking the ball was a homer when it left his bat, did not immediately run hard and ended up being thrown out at second.
A crew chief review of the play confirmed the ruling on the field that the ball hit below the yellow line and though Cabrera was out at second, Jackson scored what proved to be the game-winning run.
Verlander (9-8) went 6 2/3 innings and allowed three runs on six hits while walking three and striking out five in picking up the win.
The D-backs had a golden opportunity to at least tie the game in their half of the seventh when, with one out, Ender Inciarte singled. But with Peralta at the plate, Inciarte was picked off first base by catcher Bryan Holaday. Peralta wound up drawing a walk and Hill followed with a single.
"We made a big mistake and it cost us," Gibson said of the pickoff.
Inciarte said he thought the count was 3-2, and not 2-2, so he thought the ball to Peralta was ball four and strayed off first base too far.
"I messed up," Inciarte said. "I should be aware of the situation. That can't happen to me, that can't happen to anyone. I will take the blame. This game we lost I can't say it was all because of me, but maybe it would have been a different story."