Laine tied it 1-1 at 9:14 on a power play, scoring on a one-timer from the left face-off circle off a cross-ice pass by Gaudreau.
"I saw a quick lane through the middle," Gaudreau said. "He's obviously got a great shot, so we try to find him as much as we can, and he put it in the back of the net."
Kyrou responded for the Blues to make it 2-1 at 13:38, crashing the net and redirecting a centering pass by Robert Thomas.
"It was a real strange game," Columbus coach Brad Larsen said. "… We had 11 missed shots in the first period, and five were prime scoring [opportunities] and we don't hit the net, we don't make him make a save, we don't create a rebound or nothing. So some missed opportunities there and just some blown coverage.
"It stings. It kind of leaves you with a bad taste in your mouth. Bad mistakes that cost you goals. We really hurt ourselves in that game."
Blais extended it to 3-1 at 18:07 with a one-timer from the bottom of the right circle after receiving a touch pass from Saad.
Blais has four goals in 14 games since being reacquired from the New York Rangers on Feb. 9. He did not score in 54 games over two seasons with the Rangers.
"It feels good (to get three points in the first period), for sure," Blais said. "But the most important thing is to get the win in the end. So, I'm just happy I'm playing with two good players (Saad and Schenn). They're making it easier for me."