Smoak put the Blue Jays ahead 3-0 in the top of the first inning when he cleared the fence with Billy McKinney and Kevin Pillar on base.
Gurriel led off the fourth with a solo homer to centre. After Scott Dixon made it 4-1 with a home run in the bottom of the fourth, Gurriel drove a sacrifice fly to centre in the top of the sixth that scored Smoak.
Detroit capped the scoring in the bottom of the sixth when Daz Cameron scored on Pete Kozma’s ground out.
Left-hander Ryan Borucki overcame a rough outing against Philadelphia last week to pick up the win for Toronto (3-6). Borucki struck out four over three scoreless innings while allowing two hits and three walks.
Justin Shafer earned the save.
Matt Moore picked up the loss for Detroit (6-6).