Ryan O'Reilly gave St. Louis a 4-3 lead 1:21 later, scoring off a rebound of Brayden Schenn's shot that came off a give and go with Kyrou at 12:35.
"I thought the first two periods were really good," Berube said.
The Rangers head west for road games against the Vegas Golden Knights on Wednesday and Colorado Avalanche on Friday.
"The streak we've been on the last two weeks hasn't been good, so definitely to get a win tonight, it's positive moving forward," Gallant said. "We better be ready to play on the road."
NOTES:Kreider has points in 10 straight home games (six goals, four assists), the second-longest home points streak in the NHL behind Dallas Stars forward Jason Robertson's active streak of 12. … Fox extended his home point streak to nine games (three goals, seven assists), the fourth-longest by a Rangers defenseman. Brian Leetch had streaks of 18, 15 and 12 games during his career. … New York forward Filip Chytil missed his second game with a lower-body injury. He's day to day.