Eric Robinson scored twice, and Elvis Merzlikins made 35 saves for the Blue Jackets (14-12-1), who opened a five-game road trip with a 5-4 overtime win against the Seattle Kraken on Saturday, when they also surrendered a three-goal lead in the third period.
"We know we're a good team and if we stick to it, we can finish those games out. We were doing it in the beginning of the year," Robinson said. "We've just got to grab a hold of ourselves, maybe make the simple play a couple times to get back into it and get on the forecheck and just simplify things and calm it down."
Horvat gave the Canucks a 4-3 lead on a backdoor pass from J.T. Miller after Blue Jackets defenseman Andrew Peeke was penalized for holding with 1:12 remaining.
"I knew it was going to have to be a bullet pass from 'Millsy' and he did it right in my wheelhouse and I just wanted to be strong with my stick and get it on net," Horvat said. "And thankfully it got up for me and went in."
Horvat scored his first of the game off the rush with a wrist shot over Merzlikins' blocker from just above the right face-off dot to make it 3-1 at 7:41 of the second period.
Elias Pettersson made it 3-2 on a rebound in tight at 4:07 of the third period, and Vasily Podkolzin converted a backdoor pass from Hughes at 9:35 to tie it 3-3.
Boudreau said the comeback was more impressive after defensemen Luke Schenn and Brad Hunt and center Juho Lammikko were placed in NHL COVID-19 protocol earlier Tuesday. Defenseman Tucker Poolman was pulled from the game at 15:15 of the first period and was also placed in COVID-19 protocol.
"They got the win for themselves, not for me, but it proves they have character," Boudreau said. "Sometimes people didn't think they had character at the beginning, but you can tell. This is a team with five defenseman the last 50 minutes, down 3-0, and they battled back."
Robinson made it 1-0 at 4:25 of the first period by finishing off a backhand pass from Alexandre Texier (two assists) on a 2-on-1.
Max Domi gave the Blue Jackets a 2-0 lead at 11:37 by tapping in a loose puck behind Halak.