Collin Graf put the Sharks back in front 2-1 with a short-handed goal at 17:45. Graf skated in on a rush and cut between two defenders into the slot, where he scored with a wrist shot that beat Woll over his blocker.
Alexander Wennberg extended the lead to 3-1 at 1:39 of the second period. He skated down the right wing on a 2-on-1 and scored with a wrist shot that trickled under Woll's blocker.
It was the 100th NHL goal for Wennberg, who hadn't scored since Dec. 14 (32 games).
"Yeah, about time," Wennberg said. "It feels great. It's been a while, but it's nice to see the puck go in. This is something I'll bring home and take with me."
Matthews cut the lead to 3-2 with a power-play goal at 4:46, jamming in a rebound after Marner's shot from the point got behind Georgiev.
Eklund made it 4-2 at 13:18. Woll stopped the puck on a dump-in, but his intended clearing pass hit off Eklund's skate and deflected five-hole into the net.
Scott Laughton made it 4-3 at 15:13, scoring with a one-timer from the point that beat Georgiev over his glove. It was Laughton's first goal in 10 games with Toronto since being acquired in a trade with the Philadelphia Flyers on March 7.
"It was nice for my own confidence," Laughton said. "It was nice to get one, for sure, but it would've been a lot nicer to get a win and not score."
Toffoli pushed it to 5-3 with a power-play goal at 3:02 of the third period. He scored from the bottom of the left circle off a cross-crease pass from Eklund.