Tyler Bozak and van Riemsdyk scored in regulation for Toronto, which had lost four straight since winning the Winter Classic on Jan. 1.
Toronto goalie Jonathan Bernier stopped 36 of the 38 shots he faced through overtime. He then denied Jaromir Jagr, Ryane Clowe and Reid Boucher in the shootout to get his 14th win.
Adam Henrique and Clowe had New Jersey's goals. Cory Schneider, who narrowly missed out on making the U.S. Olympic team as the third goalie, made 23 saves.
The Leafs have only two regulation victories in their past 26 games, going 9-13-4 in the stretch dating to Nov.
One night after beating the Panthers with 2 seconds left in overtime, New Jersey fell to 0-6 in shootouts this season.
This was the third game in four nights for the Devils, and that wear and tear was noticeable throughout as they lacked the jump that opponents have seemed to show against the Leafs lately. New Jersey players took four penalties—all 2-minute minors for high-sticking.
After Bernier and the Leafs survived the first 9-plus minutes being outshot 7-1, Bozak opened the scoring with 4:07 remaining in the opening period. After Phil Kessel's original shot bounced off Schneider's chest, Bozak pounced on the puck in open ice and hit the open net.
That goal seemed to spark Toronto to have at least more sustained offensive-zone time the rest of the period.
A holding penalty to Nikolai Kulemin 43 seconds into the second put the Leafs back in their own end and cost them the lead when Henrique snapped a shot past Bernier at 1:39.
The back-and-forth action continued thanks to a penalty on Boucher. Just 13 seconds after he went to the box, van Riemsdyk crashed the net, corralled a rebound of a shot by Cody Franson and scored his 17th of the season to make it 2-1.
It only took one defensive breakdown for the Devils to tie the score.
Clowe, who replaced David Clarkson after the winger left New Jersey for a $36.75-million, seven-year contract with the Leafs, had his first multi-point game of the season. The Devils signed Clowe to a $24.25-million, five-five year deal this past summer.
Bozak, who also got a five-year deal after hitting unrestricted free agency, thought he had his second goal of the night on the power play at 6:23. But referee Ghislain Hebert immediately waived it off, ruling that van Riemsdyk interfered with Schneider.
Clarkson, who was playing his second game against his former team, played just 13:28.
NOTES: Five Leafs players—Bozak, winger Jerry D'Amigo, defensemen Tim Gleason and Mark Fraser, and goaltender James Reimer—missed Sunday's morning skate with illness. All but Fraser were in the lineup. ... Schneider started for the Devils despite making 29 saves in the OT victory Saturday night at home. Coach Peter DeBoer said it's "always a decision" because of franchise goaltender Martin Brodeur but elected to go with Schneider because of his strong performance against Florida.