"It very well could've been one of those things you talk about as a momentum-changer," manager Clint Hurdle said.
Snider not only saved runs, he created them.
Gregory Polanco also threw out a runner at the plate, when Rajai Davis tried to score from second on Miguel Cabrera's single in the eighth. Even with a five-run lead at the time, the game could've become much closer.
"They left as many men on base as we did," Hurdle said. "They were a swing of the bat from being right back in the game three times tonight."
Verlander (10-11) gave up five runs on four hits and walked two before he was removed after pitching one inning with right shoulder soreness.
"Just didn't feel great," Verlander said, "and disappointing on a night that the team really needed me."
The loss, coupled with Kansas City's 3-2 win over Oakland, dropped the Tigers a half-game behind the now first-place Royals in the AL Central Division.
Pittsburgh loaded the bases against Verlander with one out in the first inning, and Marte cleared them with a triple down the left-field line. Snider drove Marte home when his grounder to first took an odd hop, and Victor Martinez couldn't glove it.
Verlander threw 40 pitches and bunted in the second before he was removed. He is scheduled to undergo an MRI in Detroit on Tuesday.
"I'd be lying if I said I wasn't a little nervous," Verlander said. "I've never been through this before."
Verlander added there was no sharp pain in his shoulder, but manager Brad Ausmus removed him from the game to risk any further injury.
Snider knocked in two more in the eighth inning off Phil Coke with his eighth homer, a two-run, opposite-field shot.
Martin hit his sixth home run of the year in the sixth inning, and Ike Davis followed with his eighth.
Snider was 3 for 5 and scored three runs.
"Just another day," Snider said. "For me, it's nice to contribute offensively, and defensively, and help this team win."
Detroit scored three runs in the sixth to get within 8-4 and knock Pittsburgh starter Jeff Locke out of the game.
Cabrera, Martinez and Torii Hunter started the inning with consecutive hits, and Cabrera scored on Hunter's double. Alex Avila drove Martinez home with a single, and Hunter scored when Don Kelly hit into a fielder's choice.
Locke (4-3) was responsible for four runs, eight hits and four walks in five-plus innings.
Tigers: Detroit placed RHP Joakim Soria on the 15-day disabled list with a left oblique strain, retroactive to Sunday.
Pirates: Pittsburgh placed CF Andrew McCutchen on the 15-day disabled list because of a broken rib. The move is retroactive to Aug. 4. ... 2B Neil Walker (back) was out of the starting lineup for the sixth straight game. ... RHP Gerrit Cole returned to Pittsburgh after making his third rehab start Sunday. He has been on the DL since July 5 with a strained right lat. There is still no timetable for his return to action.
Tigers: LHP Robby Ray (1-1, 4.70 ERA) will be recalled from Triple-A Toledo to start on Tuesday in Detroit's second of two games in Pittsburgh. In one start this season against Minnesota on May 11, Ray pitched six shutout innings.
Pirates: RHP Edinson Volquez (9-7, 3.70 ERA) starts for the Pirates after allowing one hit in seven shutout innings against Miami on Thursday. Volquez hasn't fared well against Detroit in two career starts, allowing eight runs in 9 2/3 innings.
In addition to Soria's placement on the disabled list, the Tigers optioned left-handed relievers Patrick McCoy and Blaine Hardy to Triple-A Toledo. Taking their places are RHP Justin Miller and LHP Ian Krol.
Detroit's relievers have compiled a 4.38 ERA this season, the fifth-worst in the majors.