Matthews' boyhood idol, Coyotes captain Shane Doan, scored his 400th NHL goal in his 1,500th NHL game, but Arizona (11-18-5) lost its fourth straight. The Coyotes had defeated Toronto five straight times and was 11-1-1 over the past 13 games. Mike Smith made 28 saves.
Doan and Matthews met at center ice for the opening faceoff. Matthews was trailing the play when Doan scored No. 400.
"It's an unbelievable accomplishment. I'm happy for him, but happy we got the win as well," Matthews said. "It would have been nice if I wasn't on the ice for that one. He's been so amazing … not only hockey player for this team, but in the community."
Matthews had his best moment early. He deftly kept a Coyotes turnover onside at the Arizona blue line before hitting Brown in stride at 3:04 for his sixth goal and second in as many games.
Toronto capitalized on a Connor Murphy high-sticking penalty 13 seconds in the second period to make it 2-0. Komarov parked himself in front of the net and deflected Jake Gardiner's shot past Smith at 43 seconds for his first goal since Nov. 17.
"It felt good, but it's my job to score goals," said Komarov, who had 19 goals in 2015-16 but has five after 33 games this season. "Last year, a lot of things were bouncing my way. This year is a little bit different."
Arizona made it 2-1 when Doan took a pass from Murphy and put it past Andersen at 19:16 for his first goal in 11 games.
"Hopefully this opens the door and I can get a few more," Doan said. "Obviously this was a special night for the organization and a special for [Matthews] and 1,500 (games) is special too. I wish it didn't take me this long (to get No. 400), but at least I got it."
The Coyotes weren't able to carry the momentum into the third period. They didn't get a shot on goal in an early power play before defenseman Michael Stone lost a pass at the Arizona blue line, giving Komarov a breakaway and he beat Smith between the pads at 6:26 of the third period.
"We talked about how after that goal, hopefully it gives us some juice to get going," Coyotes coach Dave Tippett said. "But a couple of mistakes wound up in the back of our net."
Nylander raced in alone at 11:31 and scored on a backhand shot to make it 4-1.