Kuzmenko cut it to 5-4 at 12:18 of the third period after receiving a spinning pass from Elias Pettersson, and Hughes tied it 5-5 at 19:06 when his point shot went in off the skate of Marco Scandella during a 6-on-5.
"I think in the third, we got a little too passive, gave up too many opportunities," said Blues forward Brandon Saad, who had two assists. "They have a lot of skill and can score goals. Obviously, [we] want to tighten that up. Regardless, we're happy to get the win."
Hughes gave Vancouver a 1-0 lead at 6:06 of the first period, finishing into an open net from the right circle on a rebound.
Alexey Toropchenko tied it 1-1 at 11:50. After he intercepted a pass by Guillaume Brisebois intended for J.T. Miller at the Canucks' blue line, he kept the puck and scored glove side on a 2-on-1 from the left circle.
"'Torpo' scored a nice goal," Berube said. "That line [Toropchenko, Nathan Walker and Tyler Pitlick] was good for us."
Faulk gave St. Louis a 2-1 lead at 16:48, scoring short side on a one-timer from the left circle.
"Our [defensive] zone coverage early wasn't good, obviously," Tocchet said.
Kuzmemko tied it 2-2 at 19:41 on a power play when he redirected a centering pass from Miller.
Vrana restored the Blues' lead to 3-2 at 7:24 of the second period. After Nick Leddy forced a turnover by Boeser along the boards, Saad passed the puck to Vrana for a one-timer from the high slot.