The Sharks opened up their lead thanks to Gomez and Burish.
Gomez took a soft slap shot from about 45 feet out that hit the crossbar and went in. Schneider appeared to be screened.
Gomez has struggled in recent years and was bought out of his contract by the Montreal Canadiens in the offseason. He was happy to sign a one-year deal with the Sharks for $700,000.
"I'm just enjoying each day now," said Gomez, who has 10 goals in his past 133 NHL games.
Niemi has been San Jose's bright light this season, and he continued his strong play. With Vancouver pressing for the winner late in the third period, he robbed Burrows and Henrik Sedin with nifty pad saves.
He had luck on his side, too, as Jason Garrison hit the post with a minute remaining.
In overtime, the Sharks killed off a two-minute Canucks power play with Gomez in the box for goaltender interference.
"What can you say about Nemo?" Gomez said. "He was definitely the story again tonight."
Vancouver, meanwhile, had plenty of chances to win, but couldn't convert on any of their five dangerous-looking power plays.
It's the sixth straight game the Canucks have failed to score with the man advantage.
"In the third period, they did everything they could but beat the goaltender," Canucks coach Alain Vigneault said of the power play. "The looks were there, the opportunities were there, their goalie made the saves."
NOTES: Sharks coach Todd McLellan earned his 206th victory with the Sharks, tying Ron Wilson for the franchise record. ... Stuart lost some teeth while killing a penalty in the third period, and blocked four shots. "He's black and blue with bruises," Burish said. "It looks like he went through a meat grinder." ... The Canucks went 0 for 5 on the man advantage, their sixth straight game without a power play goal. ... F Bracken Kearns, 31, played his first game as a Shark and the sixth of his career. Kearns is the son of former Canucks defenseman Dennis Kearns. Bracken Kearns, who was born in North Vancouver, had zero points in five games with Florida last season. ... Canucks D Keith Ballard was back in the lineup after being a healthy scratch the past two games. He left the game midway through the third period with a lower-body injury. ... Cam Barker also dressed for his second straight game, while Kevin Bieksa (groin) and Andrew Alberts (healthy scratch) did not dress. ... Martin Havlat (lower body), T.J. Galiardi (healthy scratch) and Justin Braun (healthy scratch) did not dress for San Jose.