Needing a victory to stave off a Florida sweep, the Oilers finally clicked into gear with a superb offensive display that sends the series back to Miami for game five on Tuesday, with the Panthers 3-1 ahead.
Panthers goalie Sergei Bobrovsky, outstanding in the opening three games of the series, had a miserable night, benched midway through the second period after leaking five goals from 16 shots at Edmonton's Rogers Place arena.
"It's just one win for us -- obviously we've still got to keep getting better and hopefully we'll put more of them together," Edmonton's Leon Draisaitl said.
"We played well in the first three games and probably deserved a win or two; that's just the way it goes sometimes. We're just looking to climb back into this."
Edmonton got off to a blistering start, racing into an early lead in the first period after Florida hit the post twice in the opening minutes.
Connor Brown and Mattias Janmark swept forward on a counter-attack, with Brown cleverly drawing Bobrovsky before teeing up Janmark to steer the puck into an empty net.
The Oilers doubled their advantage after 7min 48sec, with Janmark involved once again.
The Swedish center did well down the left and flipped across to Adam Henrique who deflected the puck into the goal from close range for 2-0.
Oilers fans roared their appreciation but were soon quieted when Florida pulled a goal back through Vladimir Tarasenko, the Russian wing holding off the attention of defenseman Brett Kulak to score.
Yet any home fears of a sustained Florida rally evaporated as Edmonton restored their two-goal advantage after 14:48.
Dylan Holloway collected a pass from Draisaitl and coolly lifted a shot under the lunging Bobrovsky for 3-1.
The onslaught continued in the second period, with Connor McDavid's snap shot making it 4-1 before Darnell Nurse bagged the fifth goal after 4:59.
That goal marked the end of the evening for Bobrovsky, who was yanked by Panthers coach Paul Maurice with Anthony Stolarz taking over the goaltending duties.
Florida's frustration boiled over midway through the second period and a protracted brawl ended with Edmonton handed a two-man power play with both Matthew Tkachuk and Sam Bennett sent to the box for roughing.
The Oilers duly cashed in on their numerical advantage, Zach Hyman poking home a shot to make it 6-1.
Holloway grabbed his second of the night deep into the third quarter to make it 7-1, before Ryan McLeod's slap shot completed the rout.
The Oilers are trying to become the first Canadian team to capture the trophy since the Montreal Canadiens in 1993. Six Canadian clubs have lost in the final since then.
The Panthers are in the championship series for a second straight year after falling in five games last season to Vegas.
