The crowd gave the players a loud standing ovation after the victory, which extended Winnipeg's (19-14-5) winning streak to three games.
The Leafs (18-15-5) have now lost three straight.
Toronto goalie James Reimer
, a native of Morweena, Man., faced 35 shots and also let in a goal by Andrew Ladd.
Jets winger Antti Miettinen, claimed on waivers from Tampa Bay on Dec. 13, picked up two assists for his first points with his new club. Clarke MacArthur
and Phil Kessel
scored for Toronto, which fired 24 shots at Ondrej Pavelec.
Despite not getting their first shot on net until seven minutes into the game, the Leafs finished the first period with a 1-0 lead on MacArthur's power-play goal.
Ten seconds after Ladd was put in the penalty box for high-sticking, Carl Gunnarsson
sent the puck across the crease to MacArthur, who caught Pavelec out of position at 13:59 for his 11th goal of the season.
The Jets outshot the Leafs 15-8 in the opening period and 13-4 in the second.
Winnipeg jumped out to a 2-1 lead early in the second on goals by Bogosian and Ladd.
Bogosian got things going when he scored on the power play at 2:51. Then just four seconds after a Toronto penalty expired, Ladd tapped in a Kyle Wellwood pass from behind the net to make it 2-1 at 5:26.
Toronto's top sniper quickly made it 2-2 when Pavelec couldn't snag Kessel's shot with his out-stretched glove at 7:07. It was Kessel's 21st of the season.
Wheeler broke the tie on a power play at 10:50 when a screened Reimer couldn't make the stop.
The Leafs doubled their shots on goal in the third period, but Pavelec held the line in his 32nd start of the season.
The Jets, who only play four games at home in January, hit the road for a four-game road trip that starts Wednesday in Montreal.
The Leafs host their next four games, beginning with Tampa Bay on Tuesday and Winnipeg on Thursday. Notes:
Jets forward Bryan Little (lower body) was placed on injured reserved earlier in the day. ... Winnipeg defenceman Dustin Byfuglien missed his third straight game with a lower-body injury.