Steve Bernier scored two goals in a 12-second span in the second period, leading the Canucks to a 4-2 triumph over the Edmonton Oilers.
Bernier also had an assist, Alexandre Burrows netted a goal and set up two others and Ryan Kesler added a pair of assists for Vancouver.
Sundin, meanwhile, was eased into the lineup during his first game with the Canucks.
He played for less than 12 minutes, but joined fellow Swedes Daniel and Henrik Sedin on a pair of power-play chances.
Sundin, who spent the previous 13 seasons with the Toronto Maple Leafs, became free agent and spent the offseason dithering about his future before finally signing with Vancouver on December 18.
Sundin chose the Canucks, who originally offered him a $20 million contract on July 1, over the New York Rangers.
“Of course, it’s going to be a strange feeling,” Sundin said as he looked forward to his first game in almost nine months.
“I think every player who has been traded or moved around realizes it’s part of our game. It’s a part of the business that sometimes is not that much fun but I’m really happy to be a part of the Vancouver Canucks.”
The nine-time All-Star’s tenure in Toronto ended on a sour note when the Maple Leafs’ longtime captain declined to waive his no-trade clause last season.
The 37-year-old was criticized for blocking a possible trade that could have helped the Maple Leafs build for the future.
Sundin, who had 32 goals and 78 points last season, spent the majority of Wednesday’s game centering the second line between former teammate Kyle Wellwood and Mason Raymond.