Luke Prokop scored, plus assisted on the game-winner at 7:17 of OT.
Dylan Guenther, Carter Souch and Justin Sourdif also scored for the Oil Kings, who outshot Red Deer 52-22.
Liam Keeler, Kalan Lind, Arshdeep Bains and Jhett Larson had singles for the Rebels, who scored two straight in the third period to tie the game.
Sebastian Cossa made 18 saves for Edmonton, while Connor Ungar turned aside 47 shots.
Game 4 is Wednesday in Red Deer.