The game was the first of a doubleheader made necessary by a rainout Wednesday.
Suzuki started a three-run first inning with a single and scored an insurance run after hitting a two-out double in the eighth.
The Blue Jays had pulled within 3-2 in the top of the eighth and had the bases loaded when Rajai Davis lined a shot to left that Suzuki handled for the third out.
That allowed Andy Pettitte (4-3) to collect the win in his first appearance in about three months as he recovered from a broken leg. He allowed four hits and walked two while striking out three in five innings.
Rafael Soriano pitched 1 1/3 innings for his 41st save.
The Yankees scored three runs in their first five at-bats to beat Henderson Alvarez (9-13).
Suzuki led off with a single and took third on a Nick Swisher base hit. Robinson Cano doubled in one run and Swisher scored on an Alex Rodriguez groundout. Cano reached home on Curtis Granderson's sacrifice fly.
Toronto's Brett Lawrie led off the eighth with a double and advanced on Adam Lind's single. Kelly Johnson had an RBI single. After a strikeout, Omar Vizquel doubled in the other run. After another strikeout, Soriano came on and walked Anthony Gose to load the bases before Davis's lineout to Suzuki.
Swim Week Miami Beach 2014 [PHOTOS]