Tyler Bozak had the lone shootout goal for Toronto.
Wheeler, with two, James Wright and Antti Miettinen scored in regulation for Winnipeg (15-11-2), which earned its fifth win in six games to move into a tie with Toronto (15-12-2) for seventh in the Eastern Conference standings.
Winnipeg also clinched the season series 2-1 after beating Toronto 5-2 in Manitoba on Tuesday.
In overtime, Toronto's Nikolai Kulemin had a good scoring chance early in overtime after Ondrej Pavelec came out of his net to play a loose puck, but fired a shot wide. Later, Nazem Kadri also had a good chance but couldn't pull the trigger.
Toronto's Phil Kessel forced overtime, scoring his 10th goal of the season at 5:50 of the third to make it 4-4 before an energetic Air Canada Centre gathering of 19,401 that witnessed a game that had a playoff feel and vibe to it.
Toronto's fifth straight loss tarnished an impressive return by Joffrey Lupul. The veteran forward had two goals in his first game since suffering a broken forearm in a road win over Pittsburgh on Jan. 23. Kulemin also scored in regulation for the Leafs.
Lupul's first period back was an eventful one.
He opened the scoring at 1:32 with his first goal of the season. After taking a nice setup pass from Kadri, Lupul fired a backhand past both Jets defenceman Dustin Byfuglien and Pavelec. After taking two minor penalties in the period, Lupul finished the frame by levelling Winnipeg's Evander Kane at the final horn.
Toronto outshot Winnipeg 14-11 in an entertaining opening period that also saw the Leafs' Colton Orr and Jets' Chris Thorburn square off in a solid tilt at 4:06, their second in less than a week. The gloves came off again at 8:22 when Toronto's Korbinian Holzer wanted to go with Kane. But when Kane refused, Bogosian stepped in and registered the clear decision.
Winnipeg dominated most of the second, outshooting Toronto 16-8. Wright scored his first of the season at 5:29 to make it 1-1 before Miettinen fired a shot off the post as Toronto didn't register its first shot on goal until the 6:57 mark.
Miettinen put Winnipeg ahead 2-1 at 10:36 with his second. He batted a rebound past Scrivens after the Leafs' goalie couldn't glove Byfuglein's blast from the point. Wheeler gave the Jets a two-goal advantage, firing a bouncing puck past Scrivens for his 11th at 12:03, then made it a 4-1 contest after fending off Holzer to beat Scrivens on the wraparound at 15:29.
But Kulemin and Lupul scored 25 seconds apart to make it a 4-3 game. Kulemin fired a wrist shot off the faceoff past Pavelec at 18:35 for his third before Lupul beat the Winnipeg goalie at 19:00 for his second of the game.
NOTES — Toronto players wore camo green warmup jerseys on Canadian Forces Appreciation night while the club hung King Clancy's banner at the ACC in honour of St. Patrick's Day . . . Toronto concludes its three-game homestand Wednesday hosting Tampa Bay . . . Winnipeg forward Nik Antropov played 509 games with Toronto (1999-2000 to 2008-'09) while teammate Kyle Wellwood appeared in 189 games with the Leafs (2003-'04 to 2007-'08) . . . Lupul missed 25 games recovering from his forearm injury . . . Winnipeg's Andrew Ladd came into Saturday's game leading all NHL captains with 14 goals scored.