The best-of-7 series is tied. Game 5 is at Vegas on Tuesday.
The Canadiens outshot the Golden Knights 11-4 in the first period. They kept consistent pressure on goalie Robin Lehner, who made 27 saves in his first start since allowing seven goals on 37 shots in a 7-1 loss to the Colorado Avalanche in Game 1 of the Stanley Cup Second Round on May 30.
"We talked the last two days how in Game 3 we didn't have a good start and they took it to us most of the game," Canadiens forward Corey Perry said. "Tonight, we got that jump right away, had a strong first period. We didn't get rewarded, but it led to a goal there in the second and unfortunately, bounces go either way and it wasn't our night."
Forward Paul Byron's breakaway goal gave Montreal a 1-0 lead with 1:05 remaining in the second period. The Canadiens' strong defensive effort continued, limiting the Golden Knights 12 shots through the second period.
The Canadiens had opportunities to extend the lead, the biggest being a breakaway from rookie forward Cole Caufield 7:16 into the third period. Lehner made that save, and the Golden Knights tied the game a little more than three minutes later.
"I thought we played a good game. We just need to find a way to score more goals," Canadiens defenseman Joel Edmundson said. "Overall, it was a good game. We didn't give them too much, and when we did, (goalie) Carey [Price] was there to stop it."
Richardson said they'll look at potential tweaks, but he expects the same effort, and then some, in Game 5.
"We're OK, we're all right here," he said. "I know it [stinks] as a player to put that much effort in and come out on the losing end in overtime. But you have to park it. We'll look at a few things, mostly the good things that we did tonight, and we'll try to duplicate that. I thought we had a good start, we carried the play quite a bit tonight, and we want to do that again in Game 5."