New York won its fourth in a row despite turning to a pitcher who made only his second big-league start.
Adam Warren started a game last year for the Yankees and had 24 relief appearances this season before being called on to take the mound against the Blue Jays.
Suzuki singled to left field in his first trip to the plate Wednesday, giving him 2,722 hits during his 13 years with Seattle and New York. He also had 1,278 hits while playing nine seasons with the Oriz franchise in Japan.
Alfonso Soriano hit a two-run homer in the eighth to snap a 2-2 tie. That gave Huff (1-0) the win after a five-inning stint in which he allowed a lone hit. Rivera struck out two in the ninth for his 37th save.
R.A. Dickey (7-12) gave up Soriano's home run and five other hits to take the loss.