Zubov had a dominant game with two goals and an assist, giving the Stars a chance to close out the series in Edmonton on Saturday.
That win seemed to give Dallas new life and the Stars were in control throughout in Game 5. They shut down the Oilers with their typically stifiling defense, allowing just eight shots through the first 40 minutes.
Mike Modano scored 5:34 into the second period before Zubov tallied again 5:39 into third, making it 4-0.
While the Stars never were in danger of letting the lead get away, Marty Turco allowed a pair of soft goals in the final 10:02. Mike Comrie spoiled the shutout bid before Eric Brewer made it 4-2 with 1:50.
Turco need to make just 15 saves as the Stars outshot the Oilers, 27-17.
The Oilers pulled Tommy Salo after Brewer's goal, but Manny Malhotra ended any hopes of a miracle finish by scoring into an empty net from center ice with 27 seconds left. It was Malhotra's first career playoff goal.