Brodziak set up the eventual winner in the third, stealing a puck behind the Panthers net while shorthanded and finding a wide-open Tim Sestito in front. He scored to give Edmonton a 5-2 lead.
Brodziak has had a strong camp for Edmonton and he likely increased his odds of cracking the lineup after putting home two goals in less than three minutes early in this one.
The St. Paul, Alta., native banked a shot from the side of the net off of Panthers goalie Tomas Vokoun for his first goal of the pre-season. He then added a second goal a couple minutes later, fighting off a Florida defender to bury a shot top shelf.
Ethan Moreau and Sam Gagner also scored for the Oilers.
Michael Frolick, Brett McLean, Rob Globke and Greg Campbell replied for Florida (1-1).
Vokoun, acquired from Nashville over the off-season, allowed three goals on the first five shots he faced - two to Brodziak and the other to Moreau.
Florida closed the score to 3-1 late in the first as Frolick tipped a Jay Bouwmeester point shot past Oilers starter Dwayne Roloson, who made 17 saves in the opening frame.
Florida only needed one shot to pull back within one as McLean undressed Roloson with a deke just 10 seconds into the second, making it 3-2.
But Edmonton restored the two-goal advantage late in the period. Controversial off-season signing Dustin Penner stripped the puck and left it for Gagner, the Oilers first round pick, sixth overall, at this summer's draft.
He hit Vokoun up high with a hard shot that bounced over the Panthers netminder and into the net for a 4-2 score after 40 minutes.
After Sestito's goal, Florida fought back to within one - as close as they would get.
Globke picked up a rebound on a Campbell shot and shovelled it past Oilers replacement goalie Jeff Drouin-Deslauriers, then Campbell batted a rebound into the Edmonton net a couple minutes later to narrow the score to 5-4.
Both teams return to the ice on Tuesday, with the Oilers playing host to Toronto and the Panthers travelling to Saskatoon to play the Calgary Flames.
Notes: It was the second pre-season tilt for the Panthers, who defeated the Flames 3-0 on Sunday night. . . . Off-season free agent acquisition Richard Zednik, who crashed heavily into the end boards against the Flames, skated Monday and will likely play Thursday in Chicago. Centre David Brine, who sprained his thumb in the contest, headed back to South Florida to be evaluated. . . . Prior to starting the exhibition schedule the Oilers assigned 10 players to the Springfield Falcons of the American Hockey League, returned three players to their respective junior teams and one player to Europe.