Nylander scored with a wrist shot past Price's glove on the power play to make it 3-2 at 18:00. Jason Spezza's assist on the play was his 600th in the NHL in 1,124 games.
Tavares tied it 3-3 at 19:21 when he redirected a pass from Mitchell Marner at the top of the crease during a 5-on-3 power play.
"I think we were the better team. We talked about before the game staying out of the box because that's where they get momentum, and obviously they did tonight," Anderson said. "I think anybody watching the game [knows] we were the better team out there, but we're not going to forget this one. We'll come out next time and play better."
Joe Thornton, who signed a one-year contract with the Maple Leafs as a free agent on Oct. 16, 2020, after playing the previous 15 seasons for the San Jose Sharks, had no points and two shots in 17:30 of ice time.
"Wasn't that fun? Great game. Boys were down early, but we managed to come back and what a great finish that was by [Rielly]," Thornton said. "Hearing my number 97 from St. Thomas, Ontario, announced (before the game), you can't beat that."