It was Marleau's second goal of the game, and came exactly a minute after he broke in on a clear-cut breakaway only to have his backhand gloved by Fleury.
"That wasn't my best move, that's for sure, but it was a good save," Marleau said.
Marleau's resilience resembled that of his team's, which didn't let down after allowing Pittsburgh's Tyler Kennedy to force overtime by scoring with 50 seconds left in regulation.
"It's just a sign of our perseverance," Marleau said. "You don't want to see that happen, but when it does happen, you want to see guys forget about it right away."
The decisive goal came during a scramble in front, and after Fleury stopped Couture from in close. The puck dribbled to the left of the net, where Marleau flipped it in for the surging Sharks who improved to 14-2-1 in their past 17 games.
It was Marleau's sixth game-winner of the season, and second in overtime in a span of five games, after he settled a 2-1 win at Nashville.
The Sharks extended their winning streak to five games while also vaulting a point ahead of Phoenix into first place of the tightly packed Pacific Division.
Couture, with his franchise rookie record-tying 25th goal of the season, also scored while Antti Niemi stopped 24 shots.
Kennedy scored twice for the Penguins, who are winless in their past three (0-1-2) and dropped to 2-5-2 in their past nine since Evgeni Malkin sustained a season-ending knee injury to join captain Sidney Crosby on the injury list. Crosby is out indefinitely after missing his 21st straight game with a concussion.
Penguins coach Dan Bylsma wasn't pleased with the outcome, even though the Penguins earned a point to move four points ahead of the fifth-place Washington Capitals in the Eastern Conference.
"It doesn't feel much of a consolation prize to add a point there," Bylsma said. "We think we need to play better than that to get the result we want going forward."
The Penguins might be down yet another key player after defenseman Brooks Orpik did not return for the start of the second period after taking Marleau's shot off his hand late in the opening period. Orpik skated off shaking his hand and was escorted up the tunnel.
Bylsma said he would wait until Thursday to update Orpik's status.
The new-look Penguins continue to have difficulty scoring, despite shaking up their lineup by adding forward James Neal and defenseman Matt Niskanen in a trade that sent defenseman Alex Goligoski to Dallas on Monday.
Both Neal and Niskanen made their debuts, but the Penguins extended their string to 15 games since they scored four or more goals in regulation.
Pittsburgh has been shut out three times during that span, including a 1-0 loss to Washington on Monday.
"I don't really care how many goals we score, we've just got to win," Neal said. "We played well last game, we played pretty well tonight. We need to keep playing well every night and give ourselves a chance."
Neal finished with two shots on goal, his best chance coming four minutes into the third period, when he blasted a shot on the fly from just inside the blue line, only to have Niemi get his right shoulder up for the stop. He made an even better save with 7:01 left, getting his glove up to snatch a snap shot from Kris Letang, who was driving in alone up the right wing.
Niemi sees Sharks developing chemistry during their second-half run.
"I think it comes from just being confident that we are able to do it and we trust each other," Niemi said. "We've been playing really well lately, and we've got to keep it up."
The Sharks, coming off a 4-3 win at Detroit on Tuesday, won by rallying from a 1-0 deficit, after Kennedy opened the scoring during a scramble in front at 5:48 of the first.
Couture tied it 3:01 into the second period. He's tied with the Islanders' Michael Grabner for the rookie lead in goals and also tied the franchise rookie record set by Pat Falloon in 1991. Marleau then scored 5:28 into the third period to put the Sharks ahead 2-1.
- In closing a brief two-game homestand, the Penguins hit the road for a five-game swing that opens at Carolina on Friday. The home games are the only two for Pittsburgh during a 25-day span.
- The Sharks conclude a three-game road trip at Calgary on Friday before returning home for a six-game homestand, which opens Tuesday against Colorado.
- For the second consecutive home game, the start of the second period was delayed because the house lights wouldn't come on in the first-year Consol Energy Center. The delay on Wednesday lasted more than 15 minutes, or 10 minutes longer than on Monday.