Brock Boeser and J.T. Miller each added a goal for the Canucks (17-18-3), who snapped a three-game losing skid and won their first game of 2023.
Mikko Rantanen and Samuel Girard replied for the Avs (19-15-3).
The Avs are now winless in five games (0-4-1) for the first time since a tough stretch from Oct. 26 to Nov. 5, 2019.
Colorado pulled Georgiev in favour of the extra attacker with just over two minutes on the clock.
Pettersson picked up a loose puck in the neutral zone and sliced a cross-ice pass to Miller, who popped a short-range shot into the yawning net 18:24 into the third period.
The empty-net strike marked Miller's 14th goal of the season.
Avs centre Darren Helm got a clear breakaway with 2:16 left in the game, but Delia swallowed up his wrist shot to preserve the home side's lead.
After sputtering through the first half of the game, the Canucks erupted with three unanswered goals in two minutes and 33 seconds in the middle frame.
Kuzmenko sparked the offence with a power-play goal 13:15 into the second, shovelling a backhanded shot in past Georgiev from the top of the crease after Toews was called for hooking.
Canucks defencemen Oliver Ekman-Larsson contributed an assist on the play, marking the 300th helper of his NHL career.
A highlight reel play set up Vancouver's second goal of the night.
Putting the puck between his owns legs, Kuzmenko sprung Pettersson for a partial breakaway. The Swedish centre drove into the Colorado zone, took the puck around the net, and got off a shot as he fell to the ice. Kuzmenko then forced the puck in past Georgiev's skate, tying the game at 2-2 with his 17th goal of the season.
Boeser netted the go-ahead goal just 34 seconds later, sending a wrist shot past the Avs' netminder from in tight.
Georgiev responded by winding up and smashing his stick on the crossbar several times.
Colorado took a 2-0 lead 1:49 into the second after Girard unleashed a rocket from inside the blue line that sailed through traffic and appeared to hit defenceman Luke Schenn in the low slot on its way into the net.
An Avs power-play tally opened the scoring 19:00 into the game after Canucks defenceman Tyler Myers was sent to the box for hooking.
Stationed at the top of the faceoff circle, Rantanen fired a blistering shot through traffic for his 26th goal of the season.
WHISTLES, WHISTLES EVERYWHERE
Both sides saw their special teams tested Thursday. Vancouver went 1 for 7 on the power play while Colorado was 1 for 5 with the man advantage.
Pettersson is heading to his third NHL all-star game after being named to the Pacific Division team Thursday. The 24-year-old Canucks centre leads his team in scoring and is on pace for a career-best season with 45 points (17 goals, 28 assists) in 36 games.
— Avalanche: face the Oilers in Edmonton on Saturday.
— Canucks: kick off a five-game road swing Saturday against the Jets in Winnipeg.
This report by The Canadian Press was first published Jan. 5, 2023.
Gemma Karstens-Smith, The Canadian Press