Marner put Toronto ahead 1-0 at 15:22 of the first period, scoring with a one-timer from the left circle during a 5-on-3 power play.
The Maple Leafs outshot the Sharks 17-3 in the first period.
"I think we've just been playing really good hockey these last 10 games or so," Marner said. "We've just got to keep that going, keep that rolling."
Jarnkrok made it 2-0 at 19:17 of the second period with a turnaround shot from the left circle that trickled past Blackwood.
Nylander increased the lead to 3-0 at 9:34 of the third period when he scored blocker side with a wrist shot from the right circle.
Granlund cut it to 3-1 at 11:57, tapping in a backdoor pass from Fabian Zetterlund.
"Tonight, in the first two periods, we didn't get anything offensively," Granlund said. "We didn't get our forecheck going, we were defending a lot. So, not the way we wanted to play, but overall, our game has been better than earlier in the season. Obviously, it would be nice to try to get a win. It's not easy right now with the little streak we have, but you've got to be better than we were first two periods tonight."