Vincent Trocheck, Chris Kreider and Kaapo Kakko each scored a power-play goal for the Rangers (41-18-4), who had lost two straight. Alex Wennberg had an assist in his first game for New York after he was acquired in a trade with the Seattle Kraken on Wednesday.
"It's a dream come true playing as an away team (at Madison Square Garden), but being on the home team, Saturday night, and getting the win, can it get better than that? No," Wennberg said. "The first couple of shifts, maybe a little rusty, but for me, it felt great. Obviously, coming to a great team as well. At the end of the day, all that matters is the win and the points."
Jordan Binnington made 35 saves for the Blues (32-29-3), who lost their third straight game.
"We're not scoring," St. Louis captain Brayden Schenn said. "… If you're losing, you at least want to go down swinging, and right now, we're just not generating enough offensively."
Trocheck gave the Rangers a 1-0 lead at 5:51 of the first period with a redirection in the slot of Artemi Panarin's shot on the power play.
Jimmy Vesey made it 2-0 at 19:37, scoring with a wrist shot from the left circle on a breakaway off a stretch pass from Barclay Goodrow.
"I thought we came out great," Vesey said. "Started the game really well I thought. Obviously, it was nice to get the first goal and then be up two after one. I thought it was a good team effort."