Toronto overcame an early 2-0 deficit to win its third straight game.
Scott Richmond (7-10) left the game after five innings with a 4-3 lead and got the win thanks to outstanding relief pitching from Janssen, Josh Roenicke, Brandon League and Jason Frasor.
The relievers combined to give up a hit and one walk.
The Blue Jays broke a 2-2 tie with a three-run fourth. Travis Snider reached on a one-out fielding error by shortstop Cesar Izturis and moved to second on a balk by losing pitcher Jeremy Guthrie (10-16).
John McDonald then singled home Snider, Jose Bautista tripled home McDonald and Bautista scored on a sacrifice fly by Aaron Hill.
Guthrie missed out on a chance to reach 11 victories for the first time in his six-year career.