Shawn Horcoff scored once in regulation and again in the shootout, leading the Oilers to a 3-2 win over the Panthers for their third straight win.
"It's a good night any time you come away with two points," Oilers coach Pat Quinn said. "We just hope that continues and we find a way to keep improving as a team."
Dustin Penner also scored and Jeff Deslauriers made 33 saves for Edmonton. Deslauriers was playing in his ninth straight game while starter Nikolai Khabibulin recovers from a back injury.
Dominic Moore scored two goals for the Panthers and Tomas Vokoun stopped 26 shots.
The Oilers are on their first single-season three-game road winning streak since Nov. 13-Dec. 8, 2006. They improved to 4-4 in shootouts.
The Panthers lost for the eighth time in nine games. They failed to hold a third-period lead for the fourth time in the past five games.
"This is like Groundhog Day," Panthers coach Peter DeBoer said. "I thought we played a pretty good game. I think most nights that you play like that you're going to win."
Edmonton's Robert Nilsson and Florida's Rostislav Olesz each had shootout goals before Horcoff's decided it.
"It's always nice to have your number called and produce in a shootout," Horcoff said. "You'd like to get it done before that, and we had our chances in the overtime, but you'll take the points, for sure."
Moore gave the Panthers a 2-1 lead on a power-play goal at 1:25 of the third. As players from both teams fought for the puck in front of the Edmonton goal, Moore was able to get off a shot that got past Deslauriers' glove.
The Oilers bounced back about three minutes later when Lubomir Visnovsky's slap shot from the high slot was deflected by Penner past Vokoun on the glove side to tie it 2-all at 4:33.
"We played well tonight and that took some of the pressure off me although I would like to have that first goal (they scored) back," Deslauriers said, "but you can't dwell on that."
Horcoff gave the Oilers a 1-0 lead at 3:29 of the second period on a power-play goal. Visnovsky passed from the left circle to Horcoff in front and he tipped it in over Vokoun's right shoulder as Vokoun fell backward.
The Panthers tied it less than three minutes later. Moore passed the puck from behind the net and it hit off defensemen Tom Gilbert's skate and sneaked in at 6:07.
"We have to continue to be positive," Moore said. "It's easy to get down when you don't get the results you think you deserve."
Florida's Gregory Campbell remained on the ice for several minutes after an open-ice collision with teammate Bryan Allen between the blue and red lines as the second period ended. Medical personnel brought out a stretcher but Campbell skated off the ice under his own power. He wasn't injured but was kept out during the third period as a precaution.