Boo Nieves scored the tiebreaking goal in the second period, and Mats Zuccarello scored for New York (17-14-7), which has won two straight for the first time since winning three in a row Nov. 17-21.
"Intense. It was fun. It was to fun battle," Lundqvist said. "As a goalie, when you feel the guys battle as hard as they do, you get excited. You want to play even harder. You want to make that extra save.
"We worked so hard and we came up with the big plays at the end and at the right time. That wins you a lot of games in this league."
WATCH: [All Rangers vs. Blues highlights]
Ryan O'Reilly scored, and Jake Allen made 21 saves for St. Louis (15-18-4), which has lost two in a row.
St. Louis has scored two goals the past two games on 153 shot attempts.
"It (stinks)," O'Reilly said. "You've got to put the puck in the net, especially the power play too. We've got to find a way to bury something.
"We shot a lot of pucks, and for myself, I had a lot of opportunities and made stupid plays, and not goal-scoring plays and play-making plays, just throwing it at the net at dumb times when I've got to create more. We had [offensive]-zone time, we had chances, but sometimes, for myself, I've got to make higher-end plays than just shoveling them at the net."