Mikko Rantanen added two assists for the Avalanche, who lost leading scorer Nathan MacKinnon to an upper-body injury in the second period. No word from head coach Jared Bednar after the game on how serious the injury might be.
Colorado has dropped three in row after winning 10 straight games.
Trailing 3-2 after allowing three straight goals in the second period, the Canucks tied it two minutes into the third when Sedin scored his 12th of the season on a 5-on-3 power play as he fell to the ice.
The Avalanche nearly went back ahead on a man advantage of their own, but Rantanen hit the post behind Markstrom before Sedin also clanged one off the iron behind Bernier a couple of minutes later.
Markstrom made a big stop on Colin Wilson with just more than a minute to go in regulation.
Down 2-0 after the first period, Colorado got on the board at 4:20 of the second when Erik Johnson's shot deflected off Tanev's stick in front and changed direction on its way toward Markstrom. The goalie appeared to try to head butt the puck to safety, but Compher was there to tap home his ninth.
Colorado tied it 2:02 later when Tyson Barrie's shot from the slot that was stopped by Markstrom bounced off Landeskog and in for his 18th.
Vancouver failed to connect on consecutive power plays despite a number of chances, and the Avalanche made the Canucks pay when Landeskog scored his second of the night on a Colorado man advantage at 15:05 with a shot that got stuck behind the middle post in Markstrom's net.
MacKinnon, second in NHL scoring behind Tampa Bay's Nikita Kucherov with 61 points, was hurt shortly thereafter on a hit from Canucks defenseman Alexander Edler. The 22-year-old appeared to be favoring his left shoulder on the bench before heading to the locker room.
The Canucks opened the scoring at 6:36 of the first after the Avalanche turned the puck over at the offensive blue line.