Joe Pavelski scored his second power-play goal of the game to tie it with 4:27 left in regulation. Brent Burns also scored for the Sharks, who will now get a break before beginning the second round of the playoffs next week.
"A win like this feels good, now we will get some rest," Pavelski said.
Cory Schneider made big stops early in the overtime, but gave up the rebound that led to Marleau's series-clinching goal.
With Daniel Sedin sent off for boarding Tommy Wingels, the Sharks came through with their third power-play goal of the night to win it. Joe Thornton's shot hit off Schneider and the puck was bouncing in the crease when Marleau just got his stick on it to score the winner, setting off a wild celebration at the Shark Tank and sending Vancouver to another early playoff exit.
The Canucks have lost 10 of their past 11 playoff games to raise major questions about the future of a franchise that made it to Game 7 of the Stanley Cup finals just two years ago.
Vancouver lost the final two games of that series to Boston to miss out on the first title in franchise history. It fell in five games as the top seed in the Western Conference to eventual champion Los Angeles in the first round last year and was blitzed by the sixth-seeded Sharks this year.
The Canucks have scored just 18 goals in their past 11 postseason games and that futility could end up costing coach Alain Vigneault his job among other possible offseason changes.
Stars Daniel and Henrik Sedin did not score a goal all series and the Canucks were unable to stay out of the penalty box or hold late leads.
Vancouver took the lead with two goals in a span of 1:50 midway through the third period. The first came on the power play when Andrew Desjardins was sent off for roughing. Henrik Sedin set up the tying goal with a nifty blind pass to twin brother Daniel, who fed Burrows in front of the net for the easy tap-in.
Then Burrows won a battle for the puck in the corner and fed Edler in the high slot for a slap shot. It beat Antti Niemi and gave the Canucks their first lead since Patrick Marleau's tying goal in the final minute of regulation in Game 2 in Vancouver.
But just as in Game 2, Vancouver couldn't hold on to a late lead after Kevin Bieksa was sent off for cross-checking Wingels. Bieksa complained on the off-day that the Sharks embellished penalties and lacked integrity, making his infraction even sweeter for the sold-out crowd that booed him all night.
Bieksa could only watch from the penalty box as Pavelski pounced on a rebound of Logan Couture's shot and knocked a backhand into the open net for his fourth goal in the past two games.
Pavelski did not record a point a year ago when San Jose was knocked out in five games in the first round by St. Louis, but is a major reason why the Sharks are back in the second round for the third time in four seasons.
"We learned a lot in the third period, allowed them back in it," he said. "But our power play came through and we're here."
Vigneault stuck with Schneider one game after he was pulled in the third period after allowing five goals on 28 shots.
The move didn't pay immediate dividends as Vancouver fell behind after the opening period for the third straight game. The Sharks struck quickly when Burns tipped in a point shot from Scott Hannan less than three minutes into the game.
The Canucks tied it when Raymond's shot from inside the blue line hit off Sharks defender Brad Stuart and beat Niemi.
Stuart was involved in San Jose's second goal when he took a boarding penalty from Derek Roy in the neutral zone, just the latest unnecessary penalty by the Canucks. The Sharks made Vancouver pay when Pavelski got the rebound of Marleau's point shot, spun around and beat Schneider.
The Canucks were swept in a best-of-seven series for the fourth time and first since the 2001 first round against Colorado. ... The Canucks dressed F Steven Pinizzotto in place of Tom Sestito on the fourth line.
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SAN JOSE, CA - MAY 07: Joe Pavelski #8 of the San Jose Sharks celebrates with teamates on the bench after scoring...