De Rosa slammed a 3-1 pitch from Brad Boxberger (0-1) into upper deck leading off the 11th, breaking a 4-4 deadlock.
The Blue Jays bullpen hurled nine innings of shutout relief after starter Ramon Ortiz left the game in the third inning with an apparent elbow injury, allowing four runs.
Casey Janssen (1-0) pitched a scoreless 10th to earn the decision and Aaron Loup picked up his second save as the Blue Jays avoided a three-game sweep.
Padres starter Edinson Volquez cracked a three-run homer.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys