Schenn’s breakaway goal put St. Louis ahead 1-0 at 8:47 of the first period for his 600th NHL point (246 goals, 354 assists).
“I think the structure kind of falls out the window a little bit when you play games like that, it's back and forth and goals are going in,” Schenn said. “But at the end of the day, we got two points and we'll move on.”
Bjugstad’s wrist shot from the left face-off circle tied it 1-1 at 10:40.
The Blues regained the lead 2-1 at 12:15 on Parayko’s slap shot from the right point.
After Saad couldn’t score on a 2-on-1 rush, Jason Zucker made it 2-2 at 18:06 on a tip-in.
Lawson Crouse’s ninth goal in 11 games gave Arizona a 3-2 lead 22 seconds into the second period.
Leddy scored short-handed to tie it 3-3 at 3:40 before Toropchenko restored the Blues lead at 4:13 on the same power play.
It was their sixth short-handed goal of the season, tying the Dallas Stars for most in the NHL.
“We want to stay aggressive on the penalty kill and do things the right way, and we got rewarded for doing things right,” Toropchenko said.