DeBrusk beat Jordan Binnington in the third round of the shootout to give the Canucks their second win in six games.
Kevin Lankinen made 36 saves for Vancouver.
Sherwoodâ€s third goal came with 12:56 remaining in the third period. He picked up a loose puck in the right circle after a stick was broken and whistled the puck over the shoulder of Binnington, who finished with 15 saves.
It was his second career hat trick. Sherwood has scored nine goals this season.
Jimmy Snuggerud, Dylan Holloway and Pius Suter scored for St. Louis, which outshot the Canucks 39-18 but extended its winless streak to six games.
It was Vancouverâ€s second win in its last seven games against St. Louis.
The Blues tied it at 3-all when Pius Suter scored on the power play midway through the third period.
The Blues went ahead 2-1 on Snuggerud’s power-play goal 58 seconds into the second. Sherwood scored his second goal on a breakaway midway through the period to tie it 2-2.
St. Louis went ahead 1-0 when Holloway netted a wrist shot from the right circle early in the first. Vancouver tied it on a power-play goal by Sherwood.
Canucks right winger Brock Boeser took a puck to the midsection 33 seconds into the game. He did not return.
Canucks: At Minnesota on Saturday.
Blues: At Columbus on Saturday.
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