Conor Garland had a goal and an assist for the Coyotes (4-5-1), who were outscored 13-7 in three previous losses on the road.
"We played a really good game, 55 minutes we played really well," Raanta said. "We blocked shots and did everything right, and then last five minutes wasn't that great anymore.
"But I felt good. I've been trying to get that game-like feeling out there in practice. It's always hard to come in from a little break, but I've been doing a good job in practice, and it helps to go into a game."
It was Raanta's second start of the season and first since Jan. 16 because of an undisclosed injury.
Mike Hoffman scored two goals, and Jordan Binnington made 26 saves for St. Louis (7-3-1), which had its four-game winning streak end.
Arizona led 3-0 before Hoffman scored with Binnington pulled for an extra attacker at 16:45 of the third period to make it 3-1.
It was another slow start for the Blues, who were outshot 11-2 to begin the game and fell behind 2-0 in the first period. They were outshot 11-1 by the Coyotes to begin the game here Tuesday and trailed 1-0 but came back for a 4-3 win.
"I don't have the answer for you," St. Louis coach Craig Berube said. "You'll have to ask the players that. They're the ones that play.
"It does have to come from each individual, and I believe there's a bunch of individuals in there that do compete and work and are ready to play, but we have too many that aren't. If that's the case, you're going to have a tough time winning. That's the bottom line."
The NHL announced during the game that the Blues and Coyotes will play two games here Saturday and Monday that initially were scheduled for March 29 and 31. The Coyotes were supposed to play at the Minnesota Wild on Saturday and Sunday, and the Blues were scheduled to host the Colorado Avalanche on Saturday and Sunday, but those games were postponed because of NHL COVID-19 protocol.
Tyler Pitlick gave Arizona a 1-0 lead at 9:32 of the first period when he redirected Drake Caggiula's pass from the left corner.