Henrik Sedin scored a breakaway goal with 1:30 left in overtime, and Luongo became the Canucks' single-season victories leader with 25 saves in Vancouver's fifth straight win, 2-1 Friday night.
Luongo and the Sharks' Evgeni Nabokov, who made 35 saves in another outstanding performance following back-to-back road shutouts, were both sharp.
But thanks to Sedin's alert goal, Luongo earned his 39th victory to break Kirk McLean's franchise record for wins with 24 games still left in his dynamite debut season with the Canucks. He made only a handful of tough saves, but kept his cool when his helmet came flying off during an early goal-mouth scramble.
"It felt unbelievable, like a playoff game," said Luongo, who spent his first six NHL seasons on miserable teams in New York and Florida. "The atmosphere in the building, that type of game ... we're comfortable in these situations. We've showed it all year. It was one of our better games of the year."
Luongo might not be far off in his Shark Tank prognostication: These clubs meet each other again in San Jose on the final weekend of the regular season, and there's a decent chance they'll see each other in the first round of the playoffs.
Taylor Pyatt's goal early in the third period ended more than eight periods of scoreless hockey by Nabokov, but captain Patrick Marleau tied it with a snappy power-play goal with 6:58 left.
Sedin then got a sharp pass from Kevin Bieksa and sneaked behind new Sharks defenceman Craig Rivet late in overtime, slipping the puck under Nabokov and then poking at it again until the officials called it a goal.
The game-winner was redemption for Sedin, who was in the penalty box on a questionable high-sticking call when Marleau scored. Sedin specializes in setting up others, as evidenced by his 55 assists and nine goals.
"It banked off him and took a bounce," Sedin said. "I forgot about that (third-period) penalty. You've got to be willing to put that behind you. We've got a great team right now. Every line is getting it together."
After sitting out Thursday night's 4-2 win at Phoenix, Luongo returned to the lineup for a chance to surpass McLean's 38 victories in 1991-92.
Pyatt's rebound goal in front of Nabokov broke open a scoreless game and ended the goalie's scoreless streak at 166 minutes, seven seconds - more than 19 minutes better than his own franchise record. Counting the brief periods when Nabokov was off the ice in the previous three games, the Sharks hadn't allowed a goal in 167:16, also a club record.
"It was tough playing against them," Nabokov said. "We couldn't get going. We were trying hard, but they were plugging the zone. We scored on the power play, but other teams we couldn't find our shots."
The Sharks seemed unlikely to beat Luongo - but Marleau beat two defenders on the left wing for his first goal since Feb. 13 and his team-leading 30th of the season. Marleau recently missed five games with injuries.
With fellow Sharks goalie Vesa Toskala still nursing a groin injury, Nabokov played his 12th straight game. After alternating starts with Toskala all season, Nabokov has rounded into top form with his first consistent playing time in more than a year.
Nabokov was outstanding again, but the Sharks faltered in their return from a road trip that ended with consecutive shutouts of Dallas and Minnesota, breathing life back into their faint Pacific Division title hopes.
"We need more guys playing with a sense of urgency that just doesn't show at home the way it does on the road," Sharks coach Ron Wilson said. "It seems that we're much more focused and intense in road games. Maybe we're more afraid of losing. We should be more physical and a whole lot angrier."
Notes: Nabokov set the previous shutout record in February 2003. The goalie already is the franchise leader in nearly every career statistical category. ... Marleau's career goal-scoring record is 34, set last season. ... Pyatt never scored more than 14 goals in his first five NHL seasons with the Islanders and the Sabres.