Tyler Bertuzzi scored his first goal with the Maple Leafs to extend the lead to 4-1 at 3:35 of the second period. He swatted in a bumper pass from Jarnkrok from in front on a power play.
Matt Boldy responded 34 seconds later to make it 4-2.
Rossi, who was playing in his 23rd NHL game, then cut it to 4-3 at 9:51 when he batted in a rebound at the top of the crease.
Jarnkrok answered to make it 5-3 at 9:54 of the third period, tapping in a centering pass from Morgan Rielly.
Matthews completed the hat trick with a backhand on a wraparound to push it to 6-3 at 10:25.
“It’s been special,” Rielly said of Matthews. “He’s feeling it and has had a good start to the season, so when your guy is doing that and controlling the game, putting the puck in the net, it gives us a good chance to win.”
Nylander made it 7-3 at 12:14, beating Gustavsson short side from the left circle.
Brandon Duhaime scored at 17:32 for the 7-4 final.
“Just a couple of bad bounces," Duhaime said. "They got a couple (in the third period) and got the momentum right away, so we’ll watch the tape and address it, but not our best effort."
NOTES: Matthews is the first Maple Leafs player to score at least five goals through the first two games of a season since Wendel Clark in 1991-92 (five goals in two games). ... It was Matthews' 61st multigoal game, tying him with Mats Sundin for third in Toronto history. ... Boldy left at 10:11 of the third period because of an upper-body injury. Evason said he will be reevaluated on Sunday.