Brian Little and Jacob Trouba scored in the first period, and Olli Jokinen had a goal in the third to give the Jets some cushion. Ondrej Pavelec stopped 23 shots for Winnipeg, which was eliminated from playoff contention on Thursday.
Phil Kessel tied a career high with his 37th goal and Nazem Kadri also scored for Toronto, which remained at 84 points. The Leafs have just three games remaining and trail Columbus by one point for the Eastern Conference's last playoff spot. The Blue Jackets have five games left.
James Reimer finished with 37 saves for the Leafs.
The loss dropped Toronto into a tie with New Jersey, which beat Carolina for its third win in four games.
Jets coach Paul Maurice said earlier Saturday he was starting Pavelec in goal over rookie Michael Hutchinson because the Leafs and the other teams in the playoff race deserved Winnipeg dressing its ''best lineup.'' That lineup did not include star winger Evander Kane, who was made a healthy scratch.
Kane has two goals and eight assists in 18 games since the end of the Olympic break. Devin Setoguchi, a healthy scratch for four of the past five games, replaced him.
Playing their final home game of the regular season, the Leafs didn't need long to infuse some energy into the crowd of 19,544. Kessel gave Toronto a 1-0 lead just 2:45 in, scoring on a 2-on-1 thanks to a perfect pass from Tyler Bozak.
A missed assignment in the defensive zone cost the Leafs the lead. Somehow, Little was left all alone in the left faceoff circle, and Michael Frolik found him for his 23rd of the season at the 6:22 mark.
Reimer robbed Matt Halischuk on a 3-on-2 rush at the midway point of the period to keep it tied, and then Kadri scored an unassisted goal that Pavelec should get some credit for. Following a dump-in on the power play, the Jets' goalie went behind the net to stop the puck in nonchalant fashion.
When Pavelec muffed it, Kadri pounced and put it into an empty net with 6:15 left in the first.
The Jets then tied it in the closing seconds of the period as Trouba got positioning on James van Riemsdyk at the side of the net and banged a shot past Reimer with 3.2 seconds to go.
Reimer has now given up 13 goals in the first period of his past six starts, all regulation losses.
Two second-period power plays couldn't generate anything positive for the Leafs, who also slogged through a shot drought of 7 minutes, 24 seconds. Meanwhile, the Jets took advantage of a penalty on Paul Ranger.
With Ranger in the box for hooking Adam Pardy, Enstrom faked a shot at the blue line, waited for a screen and fired a shot past Reimer 28 seconds into the power play at 17:02.
The Leafs couldn't do anything with their late second-period power play and were outshot 26-15 through two.
Then the Jets added insurance 7:09 into the third when Blake Wheeler found Jokinen wide open in front. The goal was Jokinen's 18th of the season.
NOTES: Joffrey Lupul, who Toronto coach Randy Carlyle considered doubtful to play a day earlier, was in the lineup after missing Thursday's game with a lower-body injury. But he left the game in the third period. ... Winnipeg's Dustin Byfuglien left the game in the second period with an upper-body injury and did not return. ... Legendary Leafs G Johnny Bower was interviewed on the video board and said that a woman who was proposed to minutes earlier wearing his No. 1 jersey was actually his granddaughter. Bower then got a standing ovation following a video tribute.