Khabibulin turned aside all 19 shots he saw and rookie Ryan Nugent-Hopkins collected a goal and an assist for the Oilers, who broke a two-game losing streak with the home victory.
Corey Potter got the other goal for Edmonton.
The Rangers' Henrik Lundqvist finished with 22 saves over two periods before being lifted due to cramping.
Martin Biron made his first appearance of the year in net for New York, stopping three shots in the final frame.
Swim Week Miami Beach 2014 [PHOTOS]