Eddie Rosario launched a pair of long homers but the Twins were again done in by poor pitching.
Michael Pineda gave up a homer in the first and then got thumped with five more runs in the fourth inning, leaving with a final line of six runs on seven hits, one walk in just 3 1/3 innings. His struggles put the Twins in a 6-3 hole.
The backbreaker was a 3-run double by Toronto's Eric Sogard.
Ryne Harper was credited with 3 1/3 scoreless innings of one-hit ball before Tyler Duffey gave up a homer to Teoscar Hernandez to put the Blue Jays up 7-3 in the eighth inning.
Rosario's second homer of the game – sixth of the season – cut the lead to three, but that's as close as Minnesota would come.
Minnesota lost three of four to Toronto to fall to 9-7 on the season.
Up next: Twins at Orioles, Friday at 6:05 p.m.