It was the 10th career game for Snuggerud, who was selected in the first round (No. 23) of the 2022 NHL Draft.
Brayden Schenn had a goal and assist, Jake Neighbours scored and Jordan Binnington made 27 saves for the Blues (2-1-0), who swept a two-game Western Canada road trip after losing their season opener at home to the Minnesota Wild on Thursday.
Kiefer Sherwood scored twice, and Kevin Lankinen made 30 saves in his first start of the season for the Canucks (1-2-0), who have lost two in a row.
Snuggerud put the Blues ahead 1-0 at 8:48 of the first period, spinning around at the bottom left hash mark for a short-side wrist shot up over the blocker of Lankinen.
Schenn extended it to 2-0 at 2:10 of the second period with a high-glove one-timer from the slot after Jordan Kyrou pulled up on a partial breakaway and spotted him unchecked on what turned into a 3-on-3 rush.
Sherwood cut it to 2-1 at 5:33, chipping a backhand past Binnington from the slot.
Snuggerud made it 3-1 on the power play at 8:13 into an open net to Lankinen’s left after Pavel Buchnevich lost the puck trying to attack from the other side. It was the first goal Vancouver has allowed on the penalty kill this season after going 9-for-9 in its first two games.
Sherwood’s second goal of the game at 12:12 cut it to 3-2 on a short-handed breakaway after deking to his forehand.
Nick Bjugstad made it 4-2 on a 3-on-2 rush at 13:45, one-timing a cross-ice pass by Nathan Walker from the top of the left circle before Lankinen could get across.
Neighbours scored into an empty net from just outside the St. Louis blue line at 17:47 of the third period for the 5-2 final.