Edmonton's Ryan Jones scored on a power play 1:54 into the final frame to erase a 2-1 deficit and Petrell put the Oilers ahead to stay 35 seconds later when he stripped Randy Jones of the puck at the blue line, skated in alone and scored.
Petrell added a helper while Taylor Hall also notched a goal and an assist for the Oilers, who have won three of their last four.
Devan Dubnyk turned aside 27-of-30 shots to earn the victory.
The Jets got a goal and an assist each from Alexander Burmistrov and Nik Antropov.
Winnipeg's Ondrej Pavelec was lit up for five goals on 25 shots in Winnipeg's third loss in four games.