It was Smith's first goal since signing a two-year contract with San Jose on July 1.
"Long time coming, and to score tonight feels really good," Smith said.
Kunin made it 4-0 at 3:25 with a wrist shot from one knee. Binnington then entered in relief for St. Louis.
"The first 10 minutes of the first two periods cost us the hockey game," Blues captain Brayden Schenn said. "We didn't come out intense enough in the first period. Then in the second period, in the first 10 minutes, the compete level wasn't high enough.
“The battle level wasn't high enough and all of a sudden it was 4-0 before you know it. Tough to come back in a league like this, no matter who you're playing."
Hoffman's second goal pushed it to 5-0 at 13:45 when he scored on a breakaway.
Buchnevich scored on a wrist shot at 13:55 of the third period for the 5-1 final.
NOTES: Kahkonen posted 40-plus saves in a win for just the third time in his career (44 on Dec. 3, 2019, at the Florida Panthers; 40 on Jan. 30, 2022, at the New York Islanders). … San Jose’s three goals in the opening 3:25 of the second period were the fourth-fastest three to open a period in franchise history. The only faster instances occurred Feb. 26, 1992 (2:38 in the second against the Quebec Nordiques), Nov. 22, 2006 (2:57 in the second against the Los Angeles Kings) and Nov. 28, 1992 (2:59 in the second against the Minnesota North Stars). ... Smith became the 300th player in franchise history to score a goal for the Sharks. … Blues center Robert Thomas has 12 points (five goals, seven assists) in an eight-game point streak.