Mauer homered to centre in a four-run first off Dave Bush and hit a three-run double in the fourth that chased Guillermo Moscoso, who also allowed Morneau's homer during the seven-run inning.
Aaron Hicks, bidding to become the Twins' centre fielder, was 4 for 4 and raised his batting average to .350.
Luis Jimenez homered twice and drove in four runs for the Blue Jays.
Twins starter P.J. Walters gave up three runs and four hits in three innings.