Roberto Luongo made 27 saves in his 47th win for the Canucks, who also clinched the Pacific Division title for the Anaheim Ducks by ending San Jose's five-game winning streak.
Kevin Bieksa scored a power-play goal for Vancouver early in the third period for a 3-2 lead, but Jonathan Cheechoo tied it with a goal in traffic with 32 seconds left while Sharks goalie Evgeni Nabokov was pulled for an extra attacker.
Joe Thornton had a goal and two assists for San Jose, but finished his 114-point regular season in the penalty box after a tripping call. Ohlund's shot from the point glanced off Curtis Brown's stick and found an improbable angle into the net behind Nabokov, who made 26 saves.
Matt Cooke and Taylor Pyatt scored first-period goals for the Canucks, and Milan Michalek and Thornton tied it with power-play goals in the second.
Ohlund's goal ended San Jose's seven-game home winning streak and forced the Sharks to open the post-season on the road despite a franchise-record 107-point regular season and a conference-leading 51 victories.
By earning one point, San Jose clinched the No. 5 seed in the playoffs against Nashville, its first-round opponent last season. Dallas, which finishes its regular season against Chicago on Sunday, has 105 points but would lose a tiebreaker with San Jose on total victories.
The Sharks played without forward Bill Guerin, who sat out for the third time in four games to rest his strained groin for the playoffs.
The Canucks, who finish their regular season Sunday in Phoenix, needed just one win to hold off Minnesota for the division title - though the overtime victory ensured they won't face San Jose in the first round of the post-season. Vancouver is the only opponent to win at the Shark Tank since February, doing it twice in overtime.
Luongo is headed to his first post-season after the winningest season in history for a Canucks goalie. He broke the franchise record for wins in Vancouver's last trip to San Jose, and this victory tied Bernie Parent's long-standing, NHL single-season record of 47 wins - though it already was surpassed by New Jersey's Martin Brodeur earlier in the week.
After Cheechoo took a foolish penalty in the third, Bieksa scored on a long, low shot through traffic with 12:59 to play. Bieksa, whose hustle also was responsible for Cooke's early rebound score, got his first goal in 15 games since March 6.
Luongo seemed in control until Cheechoo slipped into the slot and swatted home a loose puck for his 37th goal, a suitable follow-up to his 56-goal campaign last season.
Notes: Six players got roughing penalties late in the first period when Thornton's hit on Alex Burrows near the benches sparked a 5-on-5 scrum. San Jose's Craig Rivet and Vancouver's Rory Fitzpatrick weren't hit with fighting majors even though they dropped their gloves and threw punches . . . Thornton left the ice with 5:06 to play after running Cooke into the boards. Both players hit the end of the rink forcefully, and Thornton was bent over in pain as he went to the locker room - but he returned to the bench moments later to assist on Cheechoo's goal . . . The Sharks finished the regular season with 27 consecutive sellout crowds.