The Twins offense continued to struggle as Toronto starter Marco Estrada (9-6) held Minnesota to one run on just two hits in 6 2/3 innings of work to pick up the victory.
It didn't take the Blue Jays long to get on the scoreboard. Josh Donaldson hit his 28th home run of the season in the bottom of the first inning to put Toronto on top.
Troy Tulowitzki made it 2-0 in the third when he also hit a solo home run off Twins starter Phil Hughes (10-7).
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Those were the 26th and 27th home runs that Hughes has given up this season. The outing snapped a streak of nine consecutive unbeaten starts by Hughes.
Hughes fought through the home runs to keep the Twins in the game. He allowed three runs on five hits in 5 2/3 innings, but the Minnesota offense remained punchless.
Minnesota will send Tyler Duffey to the mound on Wednesday for his major league debut against Toronto right-hander Drew Hutchinson.