Drake Batherson scored and Matt Murray made 22 saves in his season debut for the Senators (2-2-0). Murray missed the first three games with an illness unrelated to COVID-19.
"I've got to give them credit, they did a heck of a job getting traffic to the net," Murray said of the Sharks. "I had a real tough time seeing a lot of those point shots. That's kind of their game; they're really good at that."
Batherson elected to shoot on a 2-on-1 and his wrist shot snuck under Reimer's arm to give the Senators a 1-0 lead at 10:06 of the first.
San Jose thought they had tied the game when Labanc's long-range wrist shot beat Murray over the glove, but Senators coach D.J. Smith challenged the play for offside, and the call was reversed after a video review.
Brent Burns found Couture wide open at the edge of the crease for a tap-in to tie it 1-1 at 1:58 of the second.
"Coming to Canada is fun for a few of us who are from this area. Myself, I played junior here," said Couture, who played for the Ottawa 67's of the Ontario Hockey League from 2005 to 2009. "It adds a little extra step to your game. You want to impress people, your family, your friends that you grew up with. It's a fun trip coming out here."
Labanc one-timed a pass from Erik Karlsson on the power play to make it 2-1 at 14:36.
The Senators outshot the Sharks 11-4 in the third period.
"I think you're going to see a lot of those kinds of wins this year, where we're going to have to grind it out," San Jose coach Bob Boughner said. "Especially on the road. I think that's probably the biggest difference, that grind mentality. Last year, instead of making easy plays or the right plays, we might've tried to force it and look for offense in certain situations. Now, you've got a room full of guys that are all saying the right things and doing the right things."
NOTES: Shane Pinto left the game early in the first period, holding his shoulder after taking an awkward hit from Burns. The Senators forward returned for the second period, played one shift, left again and did not return. Smith said he was hopeful that Pinto wouldn't be out for long. … Karlsson's assist was his first point against the Senators in four games since they traded him to the Sharks in 2018.