Tyson Barrie and Ryan Nugent-Hopkins each had a goal and an assist for Edmonton (29-26-2), and Leon Draisaitl burried an empty-net strike with nine seconds on the clock. Connor McDavid helped out on all three goals.
Blake Wheeler scored the lone goal for Winnipeg (27-18-3), temporarily drawing the Jets even early in the second period with his first goal since March 26.
Oilers netminder Mikko Koskinen posted 29 saves to collect his 11th win of the season. Connor Hellebuyck stopped 24-of-26 for the Jets.
The result extended Winnipeg's longest losing skid of the season to five games. Edmonton has won four of its last five outings.
It was the final matchup of the regular season between the two teams, with the Oilers winning seven of nine games, including a decisive 6-1 victory on Monday.
Edmonton sits second in the all-Canadian North Division, seven points back of the Toronto Maple Leafs. Winnipeg is in third, three points behind the Oilers.
McDavid helped set up Draisaitl's empty-net goal, slipping the puck up the boards through the neutral zone as time ticked down. The German sniper slid a shot into the yawning net for his 24th goal of the season.
The Jets pushed hard for the equalizer in the third, outshooting the Oilers 8-1 across the first half of the period, but couldn't get a puck past Koskinen.
Winnipeg got a chance with the man advantage when Kailer Yamamoto was sent to the penalty box for slashing 15:33 into the the third.
Paul Stastny had an excellent chance in tight midway through the power play but Koskinen punched the wrist shot away with his blocker.
Yamamoto picked up the puck as he returned to the ice and streaked away on a breakaway. Hellebuyck's diving, spread-eagle save kept the score at 2-1.
The Oilers got their second power-play goal of the night 6:20 into the second after Wheeler was handed a double-minor for a high stick that left Ethan Bear with a cut over his lip.
Nugent-Hopkins wasted no time, riffling a shot in past the far post just 12 seconds into the man advantage to make it 2-1.
The Oilers forward has 14 goals on the season, including five against the Jets.
Wheeler drew Winnipeg even earlier in the middle frame after Andrew Copp forced Dmitry Kulikov to turn over the puck along the end boards.
Copp shipped the puck out to Wheeler in the right face-off circle and the Jets captain blasted a shot past Koskinen for his 11th of the season.
The Oilers opened the scoring with a power-play strike 11:52 into the game Wednesday after Wheeler was called for tripping.
McDavid sliced a pass to Barrie at the top of the slot and the defenceman ripped it past Hellebuyck into the top of the net.
The goal was Barrie's seventh of the season.
Edmonton was 2 for 3 with the man advantage Wednesday. Winnipeg was 0 for 1 on the power play.
It's a quick turnaround for the Oilers, who'll be in Calgary Thursday to face the Flames. The Jets will visit the Canadiens in Montreal on Friday.
NOTES: McDavid has 22 points (seven goals, 15 assists) against the Jets this season. He also put up 21 points (four goals, 17 assists) against the Ottawa Senators this year. ... McDavid is on a five-game point streak with five goals and 10 assists since April 10.