The anticipated pitching duel between Santana and Justin Verlander never materialized. Verlander gave up two runs in the first inning and Mauer broke the game open with his grand slam in the fifth.
Verlander (9-3) walked five batters, four of which scored, in five innings. He gave up four hits and struck out five. Santana (9-4) allowed one run, striking out six and walking one.
Justin Morneau had three hits and drove in two runs for the Twins, playing in his second game after missing almost a week because of a bruised right lung.
A leadoff single by Luis Castillo and Verlander's two walks loaded the bases with none out in the first. Michael Cuddyer drove in the first run with a fielder's choice grounder, and Morneau's infield single brought in the second run.
Detroit threatened in the first with one-out singles by Placido Polanco and Gary Sheffield. But Magglio Ordonez was called out on strikes as Polanco and Sheffield pulled off a double steal, and Santana got out of the inning by retiring Carlos Guillen on a pop fly to right.
Mauer's grand slam came with one out in the fifth after Verlander had walked the bases loaded. Mauer lined Verlander's 3-2 pitch to the opposite field and over the fence for his fourth home run of the season.
After the first inning, Santana held the Tigers hitless until Ivan Rodriguez's leadoff single in the fifth. He advanced to second on a flyout, but Santana struck out Marcus Thames and Neifi Perez to end the inning.
Polanco put Detroit on the scoreboard with his second home run, which came with one out in the sixth. He finished 3-for-4.
Jason Kubel added an RBI double in the eighth, and the Twins added four runs in the ninth on a wild pitch by Eulogio De La Cruz, an error by Perez and RBI singles by Morneau and Torii Hunter.
NOTES: Detroit third baseman Brandon Inge was a late scratch because of a lower back spasm. He was replaced in the lineup by Perez. ... Manager Ron Gardenhire said Morneau would be the DH for the entire three-game series. ... The Tigers reinstated right-hander Zach Miner (strained right elbow flexor) from the DL and placed lefty Tim Byrdak on the 15-day disabled list with left elbow tendinitis.