Stuart's goal 1:13 into overtime gave the Sharks a 3-2 victory over the Flames on Tuesday.
Stuart jumped up in the rush, drove the net and had Joe Thornton's shot deflect sharply off his elbow and past Reto Berra for the winner.
"It's been a long time since I've had an overtime goal," Stuart said. "It wasn't pretty, but I'm not going to tell anybody how it went in, it just went in."
San Jose dominated play, outshooting Calgary 35-13, yet weren't able to put the game away.
"We've had a lot of close games and just haven't been able to finish it," Stuart said. "Tonight, we let them back in it and we shouldn't have but for us to get the points, it'll be a good positive for us moving forward."
Calgary's work ethic was absent at the beginning and that was a source of frustration for the coaching staff.
"That was the biggest spanking that we've taken in the first period," Flames coach Bob Hartley said. "We didn't touch the puck. The only way that we could have touched the puck is if we would have had two pucks out there."
San Jose got a goal from Logan Couture on its second shift of the game and then a power-play goal from Patrick Marleau in the final minute, taking a 2-0 lead in a period in which they outshot the Flames 17-3.
"In the first period, we didn't see our team at all," Hartley said. "I asked (assistant coach) Marty Gelinas, should I change my lines and he said yes. I started looking and I couldn't find three guys that I felt that had decent energy."
Down 28-6 in shots after 40 minutes yet only trailing 2-0 thanks to Berra, Calgary got enough going in the third to rally and tie it.
Calgary's comeback bid began when it got its first power play of the game six minutes into the period. The Flames would need just five seconds to convert.
Rookie Sean Monahan cleanly won a faceoff from Thornton, pulling the puck back to Kris Russell and the Flames defenseman ripped a slap shot past Sharks goaltender Alex Stalock.
The goal snapped a 0-for-30 drought on the power play for Calgary that had lasted nine games and covered more than 54 minutes.
Less than four minutes later, Mike Cammalleri tied it on a backhand at 10:25.
But that momentary surge would be the long bright spot for the Flames, who were kicking off a three-game homestand.
"We're all proud people and that's been something from day one, we've been a team that played with pride and we don't want to be beat, playing in games where our shot totals look like that," Cammalleri said. "I don't see any moral victories in that."
After missing the first seven games with a hand injury, the pending unrestricted free agent leads the Flames with eight goals in 11 games.
"In the third, we were desperate and I felt that we saw our good old team again but all that said. If not for Reto Berra, the Sharks can get on the plane after the first period and they'd already have the two points," Hartley said.
San Jose (11-2-5) snapped a five-game winless skid. During the span, they had three shootout losses and one loss in overtime.
"We've been playing good hockey, we just haven't been winning shootouts. To get the full two (points), it's finally nice," Thornton said. "We had two hiccups but we played good tonight. That's how we need to play every night."
Calgary (6-9-3), kicking off a three-game homestand, is winless in its past four.
Berra's record falls to 1-2-1 while Stalock continues his unusual distinction of having won more games than he has started in his brief NHL time.
He won his NHL debut in relief on Feb. 1, 2011. Replacing Antti Niemi halfway through the second period with the Sharks down 3-0 to Phoenix, he made nine saves as San Jose rallied to beat the Coyotes 5-3.
In his first NHL start just over two weeks ago, it was a much busier evening as he was peppered for 40 shots in San Jose's 5-2 win over the Ottawa Senators.
"The other guy played pretty good. He saw a lot of rubber and played a heck of a game for them," said Stalock, the 26-year-old from St. Paul, Minnesota
"On my end, it was pretty quiet for two periods. It was a little tougher. You've got a lot more time to think about the next puck than just reacting."
Notes: Partnered most of the night with Derek Smith, Smid played 16:50. He had a penalty and was credited with two blocked shots and one hit. ... Scratched for the Flames were forwards Tim Jackman and Max Reinhart, who just celebrated his 500th NHL game. ... San Jose made two lineup changes: D Brad Stuart returned after sitting out a game and C John McCarthy was inserted. ... Mike Cammalleri is off to his fastest start since he scored 10 goals in his first 11 games in 2007-08. ... In his past five games, Niemi has a 3.82 goals-against average and .878 save percentage.