Nate Schmidt tied it 3-3 on a one-timer from the right point at 2:52 of the third, Max Pacioretty made it 4-3 at 7:02 when a return pass from Schmidt redirected off his stick into the net, and William Karlsson scored at the right post at 8:29 for the 5-3 final.
"We knew we'd see their best tonight," said Pacioretty, who finished with two goals and an assist. "We felt good about our 5-on-5 play but ran into penalty trouble and not only gave them opportunities to score, but lose our rhythm and mojo (Vegas was 3-for-5 on the penalty kill). But we were able to find it again in the third period, and lot of guys stepped up and played a really good game."
Mark Stone had three assists, and Shea Theodore had two assists for Vegas, the No. 1 seed in the West.
"I think Shea Theodore obviously is turning into a Norris Trophy-caliber defenseman; he makes big plays for us offensively," Stone said. "Our defense is transporting the puck for us to control our speed. The defense makes crisp plays and breaks out the puck well, and that leads to our transition.
"That's why you see our defense being rewarded. They're pushing the pace just as much as we (forwards) are."
WATCH: [All Golden Knights vs. Canucks Game 4 highlights]
Marc-Andre Fleury made 28 saves in his first start since a 2-1 win against the Chicago Blackhawks in Game 3 of the first round on Aug. 15.
"I knew with [Fleury] in there the guys would play hard for him, and you could tell going into the third that they were going to make a push ... they didn't like the spot they put him in in the second period," Golden Knights coach Peter DeBoer said. "He's such an important part of our group and the effort our guys gave in a back-to-back situation, third game in four nights, in the third period, showed what they think of him."
Elias Pettersson, Bo Horvat and Tyler Toffoli scored, J.T. Miller had three assists, and Jacob Markstrom made 28 saves for the Canucks, the No. 5 seed.
"We put ourselves in a [heck] of a spot to win a hockey game, get back into the series," Miller said. "It's not the third period we wanted. We had some good looks, but that's a dream spot to be in in the playoffs, to tie the series 2-2 and be up one going into the third. They had too many good looks."
Teams with a 3-1 lead are 284-29 (90.7 percent) winning a best-of-7 Stanley Cup Playoff series, including 6-0 in the first round this season.
Game 5 will be in Edmonton, the West hub city, on Tuesday (9:45 p.m. ET; NBCSN, CBC, SN, TVAS).
"I'm not looking to learn anything about our group, I know we'll come ready to go," Canucks coach Travis Green said. "It's a resilient group, they like to win. They competed hard tonight and sometimes you just don't win. We'll be ready to go next game for sure ... I'll tell you that."