Boyle put the Sharks ahead 2-1 at 9:17 of the third as diminutive Derek Roy tried to push burly San Jose forward Tommy Wingels off the puck while they were on Luongo's doorstep and two other Sharks pressured the net. Wingels sent the puck out to the high slot area and Boyle came in from the point and fired it home.
Vancouver outshot San Jose 30-28.
San Jose converted one of four power-play chances while the Canucks were blanked on two.
Kevin Bieksa scored for the Canucks before a disappointed white-towel-waving sellout crowd of 18,910 at Rogers Arena.
This marks the second time the Canucks and Sharks have met in the playoffs. Vancouver ousted San Jose in five games in the Western Conference finals in 2010-11.
The Sharks won all three regular-season meetings between the teams. The Canucks did not win a playoff game at home last spring, and have now lost five straight post-season games at Rogers Arena dating to the seventh game of the 2010-11 Stanley Cup finals.
The former No. 1 made a number of excellent saves early as the Sharks outshot the Canucks 6-1 in the first 4:06 of the game. The Vancouver goaltender got the crowd roaring as he stopped Patrick Marleau on a one-timer from the slot during a power play.
He also stretched across his crease to stop a Martin Havlat shot off a Marleau rebound.
Moments later, after the game was barely four minutes old, Luongo gloved a Joe Thornton shot from the wing while the Sharks were still enjoying their power play.
Vancouver's best chance in the first came on a Roy one-timer that Sharks goaltender Antti Niemi appeared to get a piece of before it hit the crossbar.
Bieksa got credit for Vancouver's first goal, at 12:26 of the second period, after former Canuck Raffi Torri inadvertently stuffed the puck into his own net during a scramble.
The goal ignited Vancouver's offence. Shortly afterwards, Daniel Sedin put a shot off the crossbar from a sharp angle.
But Couture forged a 1-1 tie on a power play just over four minutes later as he put a shot from the point over Luongo's blocker. Couture reaped revenge after Vancouver winger Zack Kassian took a needless roughing penalty for slamming the Shark into the boards and punching him in the head behind the play.
The Canucks outshot the Sharks 14-6 in the second period.
After Boyle scored the winner, Marleau increased San Jose's advantage to 3-1 at 14:37 of the third as he put in Couture's pass from behind the net. The shot went in off Bieksa's stick as he slid to block the puck.
Notes: Havlat left the game after the first period. ... All fans received white towels on their seats before the game. ... Canucks rookie defenceman Frank Corrado, 20, played his first NHL playoff game — only nine days after playing his first regular-season game. The Woodbridge, Ont., native has also played with Sudbury and Kitchener of the OHL and the AHL's Chicago Wolves this season. ... Rookie Joe Cannata, called up recently from the Wolves, dressed as Luongo's backup. ... Vancouver forward Ryan Kesler played after missing his club's morning skate for unexplained reasons.