Michael Amadio's power-play goal at 19:42 on a rebound from the right circle made it 5-3.
"We got away from our game plan, got away from what was working in the first period," St. Louis captain Brayden Schenn said. "They're a good team with a lot of skill and obviously know how to win. We just let them back in the game and I took a penalty and before you know it, we're down 5-3."
Karlsson scored into an empty net with 12 seconds remaining in the third period for the 6-3 final.
Vegas took a 1-0 lead at 8:03 of the first period when Zach Whitecloud's shot from the right circle went off the stick of Blues defenseman Scott Perunovich, off the crossbar and past Binnington.
"Obviously, any of us on the back end all think the same way," Whitecloud said. "Any time we can contribute, we’re happy to do it. If you keep doing the right things, then good things will come."
Jake Neighbours tied it 1-1 at 9:20 on a 2-on-1 with Pavel Buchnevich; he kept it and snapped a shot from the slot past Thompson.
Kevin Hayes made it 2-1 at 10:33 when tipped in Torey Krug’s cross-crease pass from the right circle.
Kyrou's first goal in 11 games made it 3-1 at 17:11. He picked up the puck in the neutral zone and weaved through three defenders before beating Thompson from the low slot.