Rosen extended the lead to 3-1 at 4:24, scoring his first goal of the season, and Kyrou made it 4-1 at 9:29 when he beat Saros high on the stick side.
The Blues then scored twice in 39 seconds.
Rosen's second goal made it 5-1 at 12:10, and Nathan Walker extended the lead to 6-1 at 12:49 from the slot.
Schenn's second goal made it 7-1 at 16:27 before Kunin cut it to 7-2 at 18:47 with his first goal in 10 games.
Kyrou's second goal of the game made it 8-2 at 19:13, and Dante Fabbro scored from the high slot at 12:09 of the third for the 8-3 final.
"I actually thought we played a good first, had a good period, had a lot of chances," Predators captain Roman Josi said. "Then in the second period, we just fell apart. We gave them so many chances, odd-man rushes everywhere. We left our goalies out to dry. We got embarrassed in the second period."
NOTES:The Blues scored six goals in a period three times (twice in 1984-85, once in 1990-91). ... Tarasenko had a goal and two assists to extend his point streak (15 points; eight goals, seven assists) to six games and set an NHL career-high in points (76 points; 33 goals, 43 assists). It was his 600th NHL game. … Blues forward Robert Thomas had an assist to extend his point streak to 13 games (25 points; six goals, 19 assists). … St. Louis forward Pavel Buchnevich, on his 27th birthday, had an assist to extend his point streak to 10 games (18 points; six goals, 12 assists). … The Predators had not allowed eight goals in a game since an 8-3 loss to the Edmonton Oilers on March 2, 2020. … Nashville defenseman Jeremy Lauzon is week to week with a lower-body injury he sustained Saturday. … Blues defenseman Nick Leddy did not play after taking a high stick from Wild forward Kevin Fiala on Saturday. Rosen, who replaced Leddy, had his first multipoint game in 33 NHL games. His only other NHL goal was April 1, 2019, as a member of the Toronto Maple Leafs. … Blues forward David Perron had an assist to extend his point streak (six points; three goals, three assists) to five games.