After six scoreless innings, the Mariners grabbed a 1-0 lead in the seventh on a solo homer by Justin Smoak.
But the Blue Jays quickly responded in the eighth when Brett Lawrie smacked a lead-off triple against Seattle starter Hisashi Iwakuma and came home with the tying run and one out later on a Jose Reyes single.
Yoervis Medina relieved and after retiring Rajai Davis, yielded a single to Jose Bautista. He and Reyes each moved up on a wild pitch, and Edwin Encarnacion was intentionally walked the load the bases.
De Rosa then came up to hit for Adam Lind and lined an 0-2 pitch to left, sending home the go-ahead runs.
R.A. Dickey (9-11) tossed 7 2/3 innings of one-run ball to get the win, allowing eight hits and two walks while striking out five as Toronto took the first of a three-game series.
Iwakuma (10-5) ended up yielding two runs on four hits over 7 1/3 innings.