Iafallo gave the Kings a 2-1 lead at 3:07 of the second period on a redirection in front.
Robert Thomas appeared to tie the game at 7:12, but the Situation Room overturned the call on the ice after video review showed the puck did not completely cross the goal line.
Pietrangelo tied it 2-2 on the power play at 10:16 of the second, and Thomas gave the Blues a 3-2 lead at 11:56 with his first goal of the season.
"I've been trying to get one for the last couple games, been so close," Thomas said. "After the first one got called off, that kind of [stunk], but nice to get another one.
"I missed an open net the game before. It's one of those where it will eventually come. Great play by [Zach Sanford] and I had the whole net."
Schenn's power-play goal at 7:29 of the third period extended the lead to 4-2 before he scored into an empty net at 19:01 to make it 5-2.
"Both units are doing a good job, obviously," Schenn said about the Blues' special teams. "[David Perron] made a nice pass to [Pietrangelo] there, too. Both units are going and clicking. You're not going to score every game, but you have to create some momentum along the way. And obviously tonight it was nice to get three."
Carter gave the Kings a 1-0 lead at 14:49 of the first period, but Dunn tied it 1-1 with a power-play goal at 18:23.