Thornton assisted on a pair of goals to attain a career 1,500 points in the NHL.
“I’ve played with a lot of really good teams and really good players,” said the 40-year-old forward from London, Ont.
“Fortunate enough to stay healthy a lot of years so it’s very, very special.”
Goaltender Aaron Dell from nearby Airdrie, Alta., who played his Junior A hockey in Calgary, made 30 saves for the win.
“I’ve played a few here. Some of them haven’t gone so great, so I needed this one,” Dell said.
Johnny Gaudreau countered for the Flames (27-21-6). David Rittich stopped 23 shots in the loss.
Flames captain Mark Giordano left the game in the second period. The defenceman injured his right leg lunging to launch a sharp-angled shot.
He massaged his right hamstring when he made it to the Flames bench.
After testing his leg with a short skate during a television timeout, last season’s Norris Trophy winner headed to the dressing room.
“We don’t know the extent of it. We don’t know what it is,” Flames interim head coach Geoff Ward said.
“We’ll worry about things as they unfold. Right now, it’s all speculation, so we’ll wait and see what the doctors say and go from there, but potentially it’s a huge loss.”
The Flames were looking for both a bounce-back game and precious points after Saturday’s 8-3 crumbling at the hands of the Edmonton Oilers.
Five points separated five teams atop the Pacific Division after Tuesday’s games. Calgary was fifth in that group and dropped to 1-3-1 in its last five.
“I don’t think frustration does a whole lot for you. I think anger does a lot more for you,” Ward said.
“When we’re sick and tired as a group of seeing this and losing games we’ll find a way to fix it. But more than anything, you’ve got to hate losing.”
Labanc beat Rittich with a high backhand at 7:45 of the third period.
San Jose led 2-1 at 8:02 of the second when Kane roofed the puck on a behind-the-net feed from Barclay Goodrow.
Burns drew the visitors even at 3:57, and collected his 500th career point as a Shark, with a high slapshot over Rittich’s blocker.
Thornton nabbed the puck in the neutral zone and fed Burns at the top of the face-off circle.
“He’s playing I think some of the best hockey I’ve seen him play in the last couple years,” Boughner said. “Who knows what he’s got left in the tank, but he just keeps going.”
Calgary opened the second period on the power play because of Kane’s high-sticking minor.
After the Sharks flubbed a short-handed, odd-man chance, the Flames scored on the return trip.
Gaudreau and Elias Lindholm combined on a give-and-go at 59 seconds.
The Flames outshot San Jose 16-9 in a scoreless first period.
Milan Lucic and Goodrow tangled late in the period with Lucic landing a few punches on the Shark.
Calgary’s shambolic defence against the Oilers prompted changes on defence with left-handed shots paired with righties Tuesday.
Michael Stone drew into the lineup for the first time in a month for Oliver Kylington and partnered with Noah Hanifin.
Giordano and Rasmus Andersson, and Hamonic and T.J. Brodie were the other tandems.
Notes: Sharks winger Evander Kane played his 700th career game Tuesday … Gaudreau moved into a tie for ninth in career points as a Flame joining Hakan Loob with 428.