Marner tied it 1-1 at 7:59, warding off defenseman Tyson Barrie before skating into the slot and beating a sprawling Smith.
Matthews gave Toronto a 2-1 lead at 11:08 of the first. He got the puck behind the net, skated out into the bottom of the right face-off circle, and shot short side over the glove of Smith.
"I thought we had some really, really good stretches especially early on in the first period where it seemed like we had all five guys in sync throughout all three zones and weren't giving them much," Matthews said. "There were some stretches where we got away from ourselves a bit and gave them opportunities and weren't strong on pucks. You could really go either way with it."
Turris tied it 2-2 at 1:20 of the third period when Adam Larsson's point shot deflected in off his knee. It was Turris' first game since March 8.
"You need [depth scoring]," Tippett said. "We got a break on Turris' goal, but I was happy for Turris. He's gone through a lot between struggling early, played a couple strong games for us, and then got quarantined for a while. If one deserved to have one go off (them), it was him, so it was good to see it go in for him. But that depth scoring, you need to have guys chip in from all over the place in tight games. McDavid and [Leon] Draisaitl are going to do their share, but the more people who can chip in, the better."
NOTES: Nurse's overtime goal was the third of his NHL career, tying him with Eric Brewer for the most by a defenseman in Oilers history … Keefe said he expects goalie Jack Campbell, who did not dress against the Oilers, to play against the Winnipeg Jets on Wednesday.