Chicago limited New York to 19 shots on goal, including one in the third period, and Corey Crawford got his third straight win in his fourth start of the season.
"We played great," said Crawford, who had an assist on Jonathan Toews' goal to make it 1-0 2:55 into the game. "They didn't really throw a lot of pucks toward the net. In some ways, that could be tough if] we're not really getting that much action, but, I mean, we've played great."
***[WATCH: [All Rangers vs. Blackhawks highlights]*
Alexandre Fortin and Alex DeBrincat also scored for the Blackhawks (6-2-2).
Henrik Lundqvist made 32 saves for the Rangers (3-6-1) after backing up Alexandar Georgiev in a 5-2 win against the Florida Panthers on Tuesday.
New York, which played the first of a four-game trip, has not won on the road this season (0-3-1).
"It's just having the willingness to shoot," Rangers forward Chris Kreider said. "I know I passed up a couple of shots, and that's not something I usually do, I shouldn't be doing. Has to be consistent up and down. They stick to what they do well, but we need to get pucks in behind them, get on those pucks, move east to west, and hit pucks when they go north. Move pucks north-south to our D, bang pucks and get to the net."