The Oilers also surrendered both Panthers tallies in the middle stanza but Nikolai Khabibulin made five of his 26 saves in the final period to make the lead hold up.
Edmonton made the most of its chances, managing only 13 shots for the game against Florida, which was playing in its season opener and its first game under new General Manager Dale Tallon.
Marty Reasoner got both goals for the Panthers, who lost for the seventh time in eight visits to Edmonton.
Tomas Vokoun stopped 10 shots for Florida.
Notable deaths of 2014 [PHOTOS]