Jon Merrill, Jake Middleton and Mats Zuccarello scored, and Fleury made 21 saves for the Wild (5-8-4), who have lost five in a row (0-4-1), including 2-1 in a shootout to the Senators on Saturday.
"I loved the way we battled back in the game, played in the second and third," Fleury said. "Disappointed to come out on the short end.
"I'm proud of the way the guys battled, to grind and tie the game and get the point. Obviously, we want more, need more, but I think it is a step in the right direction."
Nylander had the primary assist on a power-play goal by Matthews at 12:43 of the first period that tied the game 1-1. He tied Edmonton Oilers forward Connor McDavid for the longest season-opening streak by an active NHL player set in 2021-22.
There have been seven longer points streaks to start an NHL season, achieved by Wayne Gretzky (three times), Mats Sundin, Dany Heatley, Marcel Dionne and Bill Cowley.
Matthews' 14 goals are tied with Winnipeg Jets forward Kyle Connor for the NHL lead.
Marner assisted on Rielly's goal at 4:22 of the third. He has 401 assists in 524 NHL games and is the fastest in Maple Leafs history to reach 400, besting defenseman Borje Salming (600 games).
Marner also assisted on Knies' goal that made it 2-1 at 18:23 of the first. He is the third-fastest active player to 400 assists, trailing McDavid (425 games) and Pittsburgh Penguins forward Sidney Crosby (448).
Merrill scored his first goal of the season to give the Wild a 1-0 lead at 2:37 of the opening period.
Middleton made it 3-2 at 6:10 of the third and Zuccarello tied the game 3-3 at 8:42.
"We played really well the last 40 minutes," Wild forward Marcus Foligno said. "We have a lot of good things to take away from this trip. We had some fun off the ice and found our game a little on the ice and that is what we came here to do. We could have had four points."