Stuart joined the rush and broke for the net and had Joe Thornton's shot deflect off him and past Reto Berra for the winner.
Logan Couture and Patrick Marleau also scored for San Jose (11-2-5). The Sharks snapped a five-game winless skid, although it wasn't as bad as it sounds. During the span, they had three shootout losses and one loss in overtime.
San Jose dominated play throughout the game, outshooting Calgary 35-13. The Sharks were particularly strong in the first two periods, building a 2-0 lead with a 28-6 edge in shots.
Mike Cammalleri and Kris Russell scored for Calgary (6-9-3) in the third period. The Flames are winless in their last four.
Less than four minutes after Russell broke Alex Stalock's shutout bid, Cammalleri suddenly tied the game 2-2 on a backhand at 10:25. After missing the first seven games with a hand injury, the pending unrestricted free agent leads the team with eight goals in 11 games.
The tying goal set off a deafening roar from the sell-out Scotiabank Saddledome crowd, announced at 19,289, who until the third period had very little to cheer about.
Calgary's comeback bid began when it got its first power play of the night six minutes into the third period. The Flames would need just five seconds to convert.
Rookie Sean Monahan cleanly won a faceoff from Thornton, pulling the puck back to Russell and the Flames defenceman let a slapshot go that beat Stalock, who was screened by Lee Stempniak.
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.
Berra, making his fourth NHL start and first on home ice, finished with 32 saves, to fall to 1-2-1.
Stalock finished the night with 11 saves and has the unusual distinction of having won more games than he has started in his brief NHL time.
His debut came 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 back to beat the Coyotes 5-3.
In his first NHL start just over two weeks ago, it was a much busier evening as he peppered for 40 shots in San Jose's 5-2 win over the Ottawa Senators.
Calgary's line-up was boosted by the return of Stempniak (broken foot), who missed seven games and the Flames debut for Ladislav Smid, acquired Friday in a trade with the Edmonton Oilers.
However, the injection of the two bodies into the line-up did not spark the team.
Couture scored on the second shift of the game to make it 1-0 at 1:32, before Smid had his first shift.
On its second power play of the game, the Sharks took just six seconds to connect, Marleau scoring his ninth on a set up from Joe Pavelski at 19:04.
It was the second meeting between the two teams. Last month in San Jose, the Sharks won 6-3.
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 line-up 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 last five games, Niemi has a 3.82 goals-against average and .878 save percentage. In his first 11 games, he was 1.53 GAA and ..933 SV%.