Elias Pettersson scored, and Braden Holtby made 16 saves for the Canucks (6-10-0), who have lost five in a row.
"Toronto is a great team," Pettersson said. "If you give them time and space, they'll make you pay. It's a good game, but not good enough. I don't want to talk about it anymore. It's frustrating. I hate losing."
Andersen made 26 saves in the first and second periods.
"I just feel good, I feel focused and feel like I'm moving well and tracking the puck well," Andersen said. "It's been small things and adjustments throughout the season so far, and it's been good. Guys are helping me out well and keeping things simple for me. When I'm playing my best, it looks easier than at other times."
Morgan Rielly gave the Maple Leafs a 1-0 lead at 6:38 of the first period when he scored unassisted. The defenseman collected a loose puck cleared from the slot by Canucks defenseman Nate Schmidt and shot from the right face-off dot.
Andersen made the save against Justin Bailey on a 2-on-0 with 2:19 left in the first, stretching out his left pad to keep the Maple Leafs ahead by a goal.
Pettersson tied it 1-1 at 9:59 of the second period when he scored on the power play from the high slot off a pass by Quinn Hughes from the left corner.
"We were really good," Hughes said. "It was probably our best game all year, making plays, playing confident. We were really good and we were playing with life. So yeah, it [stinks] that we lost this one."
Alex Kerfoot put Toronto up 3-1 at 9:33 of the third period, 11 seconds after Matthews' goal.
The Canucks outshot the Maple Leafs 13-4 in the first period and 27-7 through the second.
"I don't know if we could have played any better in the first two periods and probably deserved to be up more than be in a tie," Vancouver coach Travis Green said. "But sometimes when it's not going your way, you can play a really good game and not get the result you want. Tough loss. The team played very well tonight. I feel bad for our guys."
Maple Leafs coach Sheldon Keefe said he was pleased with their performance in the defensive zone despite being outplayed in the first and second periods.
"I liked the fact our guys found their way through it, but I don't like how we played and that it took us so long to adapt, but I did like that we stuck with it," Keefe said. "The No. 1 takeaway for me is that despite being grossly outplayed through the first two periods, because we didn't crack defensively other than the one clear chance in the first period Andersen made an outstanding save on, I thought it was a lot of pucks from the outside and they didn't get access to our net very well."
NOTES: Green said forward Tyler Motte will be out at least one week with a lower-body injury. He was placed on injured reserve Monday. ... The assist on Matthews' goal extended Marner's point streak to eight games (15 points; three goals, 12 assists).
