Trailing 4-3, the Canucks had a chance to tie the game when they had a two-man advantage for 1:41.
Brown was able to step out of the penalty box, pick up a loose puck behind the Canuck defence, then skate in alone on goaltender Roberto Luongo, beating him with a high backhand.
Patrick Marleau, with his first of the season, Patrick Rissmiller, Ville Nieminen, Mike Grier and Christian Ehrhoff also scored for the Sharks, who improved their record to 4-1-0.
Defenceman Kevin Bieska had a big night for the Canucks, scoring his first NHL goal on a second-period power play, and collecting two assists.
Markus Naslund, Daniel Sedin and Mattias Ohlund also scored for the Canucks, who are 2-2-1. Henrik Sedin had three assists.
Naslund's goal was his 300th as a Canuck. That ties him for the franchise lead with veteran Trevor Linden. For Bieksa, it was his first goal in his 44th career NHL game.
The Sharks - who blew a 4-1 lead and lost 6-4 to the Oilers in Edmonton Thursday - didn't look like a team playing their second game in as many nights. They used their speed to out hustle the Canucks and strong checking to create neutral zone turnovers.
On San Jose's first goal Michalek stepped around a check from Vancouver's Alex Burrows, skated into the Canuck zone and fed Marleau with a perfect pass at the corner of the net.
The Sharks went up 2-1 before the first period ended when Michalek fired a weak shot that Luongo stopped, but Ehrhoff was there to put the rebound in.
For the sellout crowd of 18,630 it was the first chance to see a Vancouver team that lost 14 players from the club that missed the playoffs last spring.
The Canucks continue to struggle to score goals. The line of Daniel and Henrik Sedin along with captain Markus Naslund managed most of the offence.
Luongo, who came to the Canucks from Florida in the Todd Bertuzzi trade, didn't have a stellar night. He looked weak on Grier's breakaway goal that made it 6-4. The Sharks also scored three goals on rebounds.
It also was a tough night for rookie defenceman Luc Bourdon. He was beaten by Marleau on the first goal, then was guilty of a turnover that led to Rissmiller scoring.
Notes: The Canucks wore their vintage blue, white and green jerseys with the hockey stick on the front for the home-opener. ...The 50-50 draw at the game was $155,133. The prize included unclaimed money from last season. ...Defenceman Sami Salo missed the game with a groin injury and is listed as day-to-day....Centre Marc Chouinard, who missed the first four games with a sprained shoulder, made his Canuck debut.