Ryan Nugent-Hopkins netted the lone goal of the shootout, ending the fourth round and sending Edmonton to a 2-1 victory over Florida on Friday.
Nugent-Hopkins outwaited Jose Theodore, and managed to slip a backhander home from the right side for the deciding tally.
Ryan Jones scored in regulation for the Oilers, who have won four of six.
Devan Dubnyk stopped 26-of-27 shots in the victory.
Jason Garrison scored for the Panthers, who were denied a chance to set a team record for consecutive wins at home. Theodore ended up with 20 saves.