Brendan Morrison also had a goal for the Canucks, who opened the season with a 3-1 victory at Detroit on Thursday night. Mark Hartigan had a goal and an assist and David Vyborny added a goal for Columbus, which fell to 1-4-1 in season-openers.
With the Canucks trailing 2-1, Sedin scored on a backhand pass from Markus Naslund with 2:11 left in regulation.
In the overtime, Sedin's twin brother, Henrik, who had two assists, took a pass from Daniel after a faceoff, skated behind Columbus goaltender Pascal Leclaire and tried a wraparound. The puck was blocked and bounced to Daniel, who pounced on it for the winner.
Despite trailing 2-0 midway through the third period, the Canucks dominated except for Columbus' two power-play goals. They outshot the Blue Jackets 44-20 after Columbus had eight of the first 11 shots.
Sami Salo's wrist shot from the right point glanced off Morrison's back and past Leclaire to cut the lead to 2-1.
The Blue Jackets needed just 1:46 to score first. With Vancouver's Kevin Bieksa off for hooking, Duvie Westcott took a hard shot from the right point that Hartigan redirected past Roberto Luongo.
Hartigan got extensive playing time because the Blue Jackets are short on centres due to injuries. Sergei Fedorov and Alexander Svitov are both out for the first three or four games because of shoulder injuries, leaving Hartigan as one of the few experienced centres on the roster.
Luongo, an off-season acquisition from Florida, made three good saves soon after the opening goal, stopping shots by former Canuck Anson Carter from the slot, Manny Malhotra on a blast from the right circle and Vyborny's shot after a Vancouver turnover.
Carter, a free-agent signing by Columbus just as camp was getting under way, played on the same line with the Sedins last season and had a career-best 33 goals and 22 assists.
The Canucks had the first 14 shots of the second period, but penalties continued to hurt them.
Rory Fitzpatrick tripped Rick Nash and Mattias Ohlund was called for delay of game after flipping the puck over the glass, giving Columbus 1:40 with a two-man advantage late in the second period.
The Blue Jackets made the most of the chance, scoring on Vyborny's hard-angle shot from the right side, the puck bouncing past Luongo off the back of defenceman Willie Mitchell's leg.
Notes: Columbus D Rostislav Klesla served the first game of a two-game suspension for a pre-season hit on Chicago's Tuomo Ruutu during a game Sept. 22. . . . The Canucks play nine of their first 11 games on the road, while Columbus plays seven of its first 11 at home.