Kevin Slowey (8-1) pitched a great ball game, throwing six scoreless innings on his way to a fourth consecutive win.
David Huff (0-2) gave up nine hits and four runs in his five innings of work for Cleveland.
The Twins scored first in the third inning on a Denard Span RBI single to right, scoring Alexi Casilla. Mauer singled later in the inning, scoring Span, making it 2-0 Minnesota.
They added another two runs on Mauer's two-run homer in the fifth inning, making it 4-0 Twinkies.
The Tribe decided to get involved in the seventh when Kelly Shoppach drove in two runs on an RBI double to right field, scoring Luis Valbuena and Trevor Crowe, making it a 4-2 ball game. Then in the eighth, Victor Martinez hit his second home run in as many nights, driving a Jose Mijares pitch into the left field stands making it a one run affair.
Joe Nathan was summoned into the game to face pinch hitter Ryan Garko with two down in the eighth and Mark DeRosa on second. After a wild pitch, DeRosa moved to third. With the count in his favor at 2-0, Garko could only manage to hit a weak roller to second, squandering a great chance to tie the game.
Nathan allowed a two-out hit to Jamey Carrol in the ninth. Ben Francisco battled back from an 0-2 count to make it 3-2, but came up just short on a deep fly ball to left field, leaving the Tribe just short of a big win.
Tony Sipp had a good relief outing for Cleveland, throwing two 1/3 innings, surrendering two walks, no hits, no runs. Aquino relieved Sipp, pitching 2/3 of an inning giving up one hit, no runs.
Cleveland will look to bounce back on Wednesday night, with their ace Cliff Lee scheduled to start.