Justin Faulk and Nick Bjugstad scored, and Joel Hofer made 32 saves for the Blues (3-7-2), who have lost seven straight (0-5-2).
“What I liked was our defensive habits were significantly better,” Blues coach Jim Montgomery said. “And I liked our first period and our third period.
“The biggest dislike from the game was too many turnovers, trying to go east-west against a team that had three back all night long. In the third period, we got in behind them and worked and forechecked and ended up generating a lot of scoring chances.
“We're trying to stay in the moment. That's the way we always are with our process. And right now, the last two games, our process has been good and as we continue to improve upon it then the results will come.”
Faulk put St. Louis up 1-0 at 3:37 of the first period. Oskar Sundqvist sent a cross-ice pass from the left boards to Faulk in the right face-off circle, who beat Greaves with a wrist shot.
Coyle evened it 1-1 at 4:38 by jabbing a loose puck in the crease over the goal line off the right skate of Faulk. Coyle also had four assists against the Toronto Maple Leafs on Wednesday.
Werenski made it 2-1 at 11:55 of the second period with a shot from the right dot that went through the legs of Blues defenseman Philip Broberg.
“(Hofer) was really good tonight,” Montgomery said. “He gave us a chance in the second period when I thought that they tilted the ice on us.
“He made several really key saves. The goals, there's not a chance he has on those goals. He made several key saves to keep it 2-1, 3-1.”
Monahan scored on the power play at 5:07 of the third period to increase the lead to 3-1. He tapped in the rebound of a Werenski shot from the point that dropped in the crease after it hit the left post. The goal was Monahan's first of the season and 600th NHL point (264 goals, 336 assists).
“I feel like I needed one,” he said. “It's nice to put one in and I mean, that seals the game so that's the biggest thing.”