Filip Forsberg, Mattias Ekholm, Colton Sissons and Calle Jarnkrok scored, and Juuse Saros made 24 saves for the Predators (10-9-3), who were outscored 30-14 during the streak (0-5-1).
"Winning's a lot more fun than losing," Nashville captain Roman Josi said. "I thought we worked really hard tonight. We can enjoy this for a couple minutes and then obviously, play them again Monday. So it's going to be even harder, but it's definitely a lot more fun."
WATCH: [All Predators vs. Blues highlights]
Klim Kostin scored his first NHL goal, and Jordan Binnington made 39 saves for the Blues (14-5-5), who are 2-2-2 in their past six following a seven-game winning streak.
"They got a couple bounces early, but even saying that, that's not our brand of hockey," St. Louis center Brayden Schenn said. "Turned over the puck too much, sat back, didn't take care of the puck and [caused] them to (have) good chances and break out with the puck. Our turnovers led to their offense and we have to clean it up for the next game."
Forsberg scored 20 seconds into the game on a rebound to give the Predators a 1-0 lead.
Ekholm made it 2-0 at 3:40 when his shot from along the left boards hit defenseman Jay Bouwmeester's stick, went off Justin Faulk in front, and deflected in off Binnington's stick.