It was Matthews' first hat trick since he scored four goals in his NHL debut against the Ottawa Senators on Oct. 12, 2016.
"My linemates made some unbelievable plays to get me the puck tonight, so I just tried to put it in," Matthews said. "Overall, we wanted to have a good bounce back game (after an 8-4 loss to the Florida Panthers on Sunday). There was a bit of a lull in the second period, some stuff we'd like to clean up and do better, but all in all, nice to get back in the win column."
[WATCH: All Devils vs. Maple Leafs highlights]
Rasmus Sandin had two assists in his first NHL game since Oct. 12, John Tavares had a goal and two assists, and Frederik Andersen made 25 saves for the Maple Leafs (25-16-6), who had lost three straight (0-2-1).
"I feel confident out there, I feel like I know all the guys a little bit more, too, so that helps," said Sandin, who was recalled Monday after Morgan Rielly fractured his foot against the Panthers that will keep him out at least eight weeks. "It's great when those two shots result in goals. Those shots weren't the hardest, but they got a stick on it and that helped our team."
Blake Coleman had a hat trick for the Devils (17-22-7), who had won two in a row. Louis Domingue allowed five goals on 19 shots before being replaced in the second period by Cory Schneider, who made 13 saves.
"Not the setting I pictured it in, but it's always special to get your first hat trick. That's the kind of line we have around our team, which is to never give up and keep pushing, so that's why I got it," Coleman said. "We want to see push back in games like this, but it's also fairly frustrating. Playing good hockey of late, (but) we didn't show up for a period and a half, myself included. For whatever reason, we were flat and a good team like that can make you pay pretty quickly."
Video: NJD@TOR: Coleman records first career hat trick
Tavares gave Toronto a 1-0 lead at 5:18 of the first period on a redirection of Sandin's point shot, and Frederik Gauthier made it 2-0 at 9:10 following a failed clearing attempt by Connor Carrick.
Zach Hyman deflected Sandin's point shot on the power play to extend the lead to 3-0 with four seconds left in the first.
"The biggest thing about Sandin's game is poise, and when you have that, you don't get fazed by where you're at," Maple Leafs coach Sheldon Keefe said. "He has that in spades, and he showed it again here tonight on those plays."
Video: NJD@TOR: Hyman nets PPG off deflection in front
William Nylander redirected Pierre Engvall's pass at the left post to push the lead to 4-0 at 2:12 of the second period.
Coleman fought off Dmytro Timashov on a partial breakaway and jammed a shot past Andersen at 6:56 to cut it to 4-1.
Matthews chipped Mitchell Marner's pass at the side of the net on the power play to make it 5-1 at 10:39, and he scored on a one-timer at 3:58 of the third period to make it 6-1.
Coleman scored on a breakaway to make it 6-2 at 12:00 before completing his hat trick at 15:35 to cut it to 6-3.
P.K. Subban scored on the power play at 18:02 to bring the Devils to within 6-4, but Matthews scored into an empty to complete his hat trick to make it 7-4 with 1:20 remaining.
"There was no life on the bench, no energy. It's no excuse," Coleman said. "We prepared the same way as we have lately, the right way, but if you're not feeling it, you have to keep things really simple and we didn't do that. We put ourselves in a hole we shouldn't have been in, and had we played the way we did the last 10 minutes, it would have been a different game."
Video: Enterprise Hat Trick: Matthews and Coleman
They said it
"For some reason, we didn't have it to start the game. We didn't have our legs, there was no spark, the energy wasn't there. I don't have the answer why, but this was two different teams from tonight to the one from our last two wins against the Washington Capitals and Tampa Bay Lightning." -- Devils coach Alain Nasreddine
"Just continue to play well, do the right things and try to win hockey games. We've got a lot of key guys out, guys who play big minutes for us, leaders on this team, so now it's an opportunity for other guys to step up and play a bigger role and try to exceed what they've done out there. It's a challenge we all should look forward to." -- Maple Leafs forward Auston Matthews
Need to know
Devils forward Jack Hughes did not play in the third period because of an illness. … Maple Leafs forward Jason Spezza played his 1,100th NHL game. … Marner has 11 points (three goals, eight assists) in an eight-game point streak.
Devils: At the Washington Capitals on Thursday (7 p.m. ET; NBCSWA, MSG+ 2, NHL.TV)
Maple Leafs: Host the Calgary Flames on Thursday (7 p.m. ET; TSN4, SNW, NHL.TV)
Video: Matthews records hat trick, Maple Leafs defeat Devils