Brad Penny (5-4) allowed three runs on eight hits over five innings to get the win, while Miguel Cabrera tacked on a solo homer in the sixth inning for the Tigers, who took two of three in the series and have won six of their last seven overall.
"You watch the game and you watch where my pitches went, they went where they were intended to go for the first three innings," said Peavy. "Then after that, I didn't really throw one ball where it was supposed to be thrown."
But the lead evaporated when Peavy unraveled in the fourth. After a leadoff single and a pair of one-out walks, Victor Martinez put the Tigers on the board with a sacrifice fly.
Andy Dirks followed with an RBI double to tie things, and Alex Avila walked in front of Raburn, who took the first pitch he saw into the bullpen beyond the left-field wall for his third career grand slam.
"It feels great, especially being able to help your team win and come through like that," Raburn said of hitting a grand slam.