Kyrou scored on a power play at 15:34 to make it 3-1, appearing to try to score through his legs before lifting a backhand over Saros' left shoulder from in front.
"Got a couple [of] low plays there and saw an opportunity to take it to the net and did," Kyrou said. "I got a good shot there.
"[Out of] the corner of my eye, I saw a little lane to the net. I tried maybe going through my legs and just brought it back to my backhand instead."
Thomas made it 4-1 at 1:03 of the third period when he and Saad each redirected a point shot by Calle Rosen, and Alexey Toropchenko scored 58 seconds later to make it 5-1, tucking the puck in following a passing play with Pitlick and Nathan Walker at 2:01.
"We know they're going to come out with everything they've got," Thomas said. "We got two quick goals in the first [two] minutes … good start for us, and that's what you need to do at the start of the third period, especially against a dangerous team like them."
Mattias Ekholm scored on a backhand with 2:08 remaining during a 4-on-4 for the 5-2 final.
NOTES:Blues defenseman Tyler Tucker had an assist for his first NHL point in his 10th game. ... St. Louis had 33 shots on goal after having fewer than 30 in seven straight. ... Josi led the Predators with seven shots in 24:51.