Johnson tied it 1-1 at 13:41 when he scored off the rebound of a Blake Comeau shot.
Colorado forward Tyson Jost received a double minor for high-sticking Pierre-Edouard Bellemare at 13:43.
Vegas went ahead 2-1 on Marchessault's power-play goal 33 seconds later, at 14:16, and Theodore scored for the first time since Jan. 2 to make it 3-1 at 1:31 of the third period.
Karlsson scored into an empty net with 16 seconds remaining to make it 4-1.
"Before this season, I didn't think I'd score 40, to be honest," Karlsson said. "I wanted to score more than six goals (his total in 81 games for the Columbus Blue Jackets last season). Safe to say I did that."
Vegas is the third Western team to clinch a playoff berth, joining the Predators and Winnipeg Jets. The Tampa Bay Lightning and Boston Bruins have clinched in the Eastern Conference.
"You look at the NHL, you look at the teams, to make the playoffs is really tough," Gallant said. "For an expansion team to make the playoffs is incredible."