Joe Pavelski scored in the closing seconds of the second period and opening minutes of the third to start San Jose's comeback and Kyle Wellwood tied it later in the third. Alex Stalock got the win in relief in his NHL debut, making nine saves, including a strong pad stop on a tip by Shane Doan on the power play shortly before Marleau's game-winner.
Keith Yandle scored to extend his point-scoring streak to 10 games for the Coyotes, but lost the puck to Marleau in the offensive zone on the power play.
Marleau then knocked the stick out of Kyle Turris' hands while getting the puck in the middle of the ice and skated in to beat Ilya Bryzgalov on the breakaway. That provided a fitting moment on a night that began with Marleau being honored in a pregame ceremony for recently playing in his 1,000th game.
Joe Thornton added an empty-net goal with 10.2 seconds to play, leading Yandle to break his stick in frustration.
The comeback sent the Sharks off on a high note for their longest road trip of the season - a seven-game, two-week trek that begins in Anaheim on Wednesday night. The Sharks have won five of six heading into the road trip, putting last month's six-game losing streak far behind them.
Radim Vrbata opened the scoring for the Coyotes and Paul Bissonnette added his first goal of the season for Phoenix, which lost to San Jose for the seventh straight meeting.
The Sharks came out flat and trailed 3-0 late in the second period. They were booed by the home crowd, pulled goalie Antti Niemi and couldn't even get into a fight when they tried.
Jamal Mayers dropped his gloves right after a faceoff midway through the second, ready to challenge Bissonnette. But Bissonnette, who has nine fighting penalties this season, didn't take the bait and Mayers was left shaking his head as he was sent to the locker room with a 10-minute misconduct penalty.
But the frustration started to ease late in the period when Eric Belanger got sent off for holding. Dany Heatley sent a shot in on Ilya Bryzgalov and Pavelski knocked the rebound in with 7.2 seconds left in the period to cut it to 3-1.
Then just 1:24 into the third, Pavelski skated to the front of the net and was in position to knock in a rebound of Devin Setoguchi's to make it a one-goal game.
Wellwood tied it with his first goal since joining the Sharks late last month off a pass from fellow newcomer Ben Eager - capping a stretch of three goals in less than 6 minutes.
The Coyotes jumped on the Sharks with two goals in a strong opening period and then took control of the game when Bissonnette scored for the first time in more than a year on a one-timer in the slot off a feed from Oliver Ekman-Larsson to make it 3-0 and draw boos from the crowd. That goal led coach Todd McLellan to pull Antti Niemi and put Stalock in goal for his NHL debut.
NOTES: Yandle has 15 points during his 10-game streak. ... San Jose leading goal scorer Logan Couture was a late scratch with the flu. ... The Sharks did not recall F Jamie McGinn from Worcester after the All-Star break. McGinn scored one goal in 49 games before the break.