Matthews passed Vaive and set the Toronto record with a power-play goal at 18:58 of the second when he scored from a sharp angle at the bottom of the left face-off circle to make it 2-1.
"It felt good," Matthews said. "Just a lot of emotions running through your mind, I guess, and just running through your body when you see the puck go in. I don't know really what else to say. It was definitely exciting and a fun moment."
John Klingberg tied it 2-2 at 5:43 of the third period on a one-timer from Robertson.
Morgan Rielly one-timed a feed from Marner to give the Maple Leafs a 3-2 lead at 10:36, but Pavelski tied it 3-3 at 17:37 on a redirection of Ryan Suter's shot.
Matthews won it when he skated with the puck from center ice, drove past two defenders and stuffed a shot past Wedgewood.
"You get into those last 10 minutes of the third period, and we got a big goal with a couple of minutes to go," Dallas coach Rick Bowness said. "You're down there, you get a point, so you take it. We were certainly going for two in overtime, we just didn't get it tonight. That was a world-class move by Matthews, a world-class player."
NOTES: It was Matthews' 52nd multipoint NHL game, passing Pat LaFontaine for the most by a U.S.-born player before age 25. He extended his point streak to 15 games (19 goals, 10 assists) and had a game-high 12 shots on goal. … Marner had an assist to extend his point streak to 12 games (eight goals, 19 assists). … Nylander has four goals and five assists during a five-game point streak. … Toronto finished 3-0-1 on a four-game road trip. … Pavelski reached 70 points for the fourth time in his NHL career. … Seguin has scored in back-to-back games.