Morneau's solo blast in the sixth inning extended the Twins' lead to 6-3 and his two-run shot in the eighth gave Minnesota its final margin of victory.
Starter Kevin Slowey (5-3) pitched well enough for the victory, surrendering eight hits and three runs over five innings. Alex Burnett, Matt Guerrier and Jesse Crain teamed up to toss four innings of scoreless relief.
Toronto's Dana Eveland (3-3) was saddled with the loss after being victimized for two unearned runs. He allowed nine hits and walked four during his four-inning stint.
Jose Bautista socked his 11th homer for the Blue Jays.