Calle Rosen scored, and Thomas Greiss made 29 saves for the Blues (35-35-6), who had scored 27 goals in their previous five games (4-1-0).
"We got what we deserved today, I think," St. Louis forward Brayden Schenn said. "I don't think we had even close to our best game and turned over pucks and lost battles and probably took a team lightly that's fighting for a playoff spot. That's what happens when you don't show up."
Novak gave the Predators a 1-0 lead at 4:46 of the first period. Evangelista sent a backhand, cross-ice pass from along the boards to Novak, who lifted in a backhand over Greiss' left shoulder.
Cody Glass, who turned 24 on Saturday, made it 2-0 at 7:20 when he redirected Novak's wrist shot from the left point.
It was the first of two power-play goals for Nashville, which had gone 1-for-29 with the man-advantage in its previous 10 games.
"I thought our energy right out of the gate was really good," Evangelista said. "It was a really good bounceback for us. We didn't play our best game in Pittsburgh (a 2-0 loss on Thursday) and we knew we needed to bounce back. We were getting a ton of shots and a ton of chances, so that contributed to our offense right away."