The Canucks' Alex Burrows had created a 2-2 tie with his 15th goal this season at 16:03 of the third period.
Vancouver's Pavol Demitra scored his NHL-leading 5th shootout goal and Toronto's Mikhail Grabovski also scored in the shootout to set up the dramatic finish.
The 38-year-old Sundin, who played for the Maple Leafs for 13 seasons, was facing his former team for the first time since leaving Toronto at the end of last season. He received a standing ovation when he was introduced.
Sami Salo and Alexandre Burrows scored one goal apiece in regulation for the Canucks, who have won five of their last six road contests.
Jason Blake and Matt Stajan both scored once in regulation for the Maple Leafs, who have lost seven of their last nine outings.
Celebrity Families of 2014 [PHOTOS]