McKenna, the No. 1 pick in the 2026 NHL Draft, had gone without a point in his first three games.
Matthews, who also had three assists, put in the rebound of William Nylander’s shot at the bottom of the right face-off circle to give Toronto the win.
Nylander had a goal and two assists, and Jack Roslovic had a goal and an assist for the Maple Leafs (2-2-0), who have had each of their four games decided by one goal. Anthony Stolarz made 21 saves.
Steven Stamkos and Nils Hoglander each scored twice, and Filip Forsberg had two assists for the Predators (1-1-1). Juuse Saros made 33 saves.
McKenna cut it to 4-3 at 14:31 of the second period when he took a pass from Matthews, who was at the right boards, and shot past Saros’ blocker from just above the right face-off dot.
The Maple Leafs tied it 4-4 at 8:54 of the third period. Roslovic took a pass from Matthews that put him in alone before he lifted a shot over Saros’ glove from the top of the crease.
Nylander appeared to put Toronto up 5-4 at 11:49 but the goal was disallowed after Nashville successfully challenged for offside.
The Predators went up 1-0 at 7:13 of the first period on the power play when Stamkos put in the rebound of Matthew Wood’s shot below the left dot. Toronto had three chances to clear the zone on the penalty kill but failed to do so each time before Stamkos’ goal.
Hoglander pushed it to 2-0 at 9:08. After Adam Wilsby’s shot banked off the end boards, Hoglander corralled it at the left side of the net and tucked it around the post with Stolarz out of position.
Hoglander scored again at 3:03 of the second period to make it 3-0, chipping in a rebound at the side of the goal crease after Filip Forsberg carried the puck to the net.
Tavares pulled Toronto to within 3-1 at 4:56. He carried the puck through the neutral zone after taking a pass from McKenna and shot over Saros’ blocker from the left dot.
Nylander made it 3-2 at 6:58 on the power play. After Saros made a right pad save on Auston Matthews’ shot, Nylander put the rebound in from the slot.
The Predators grew the lead to 4-2 at 13:30 when Stamkos shot over Stolarz’s glove from the top of the right circle.