Calling on their ace to salvage a win, James Shields delivered seven shutout innings in a 5-0 win.
Shields (10-8) gave up three hits and walked one while picking up nine strikeouts.
He was aided by three RBI from Eric Hosmer while Alex Gordon and Emilio Bonifacio each drove in another.
Blue Jays (62-75) starter J.A. Happ lasted just four innings, surrendering all five runs on six hits.
The Royals (70-66) now sit 5 1/2 games back in the AL Wild Card race and begin a four-game series against Seattle at home on Monday.