Christensen's goal for the injury-hit Rangers, without key players Chris Drury, Vinny Prospal and Marian Gaborik, came just 28 seconds after Patrick Kane had pulled the Blackhawks level at 2-2.
"It was huge," Rangers center Brandon Dubinsky told reporters. "For (Christensen) to come back and bury one right away, it felt like we didn't miss a beat."
Dubinsky scored twice on the night, his seventh and eighth of the season, as the Rangers (6-4-1) won their second consecutive game.
Chicago (7-6-1) winger Tomas Kopecky had opened the scoring at 17:13 in the first period before Dubinsky's goals at the end of the first and beginning of the third period gave the Rangers' the lead.
Ryan Callahan assisted on both Dubinsky goals to extend his points streak to seven games and pull New York within two points of the Philadelphia Flyers at the top of the Atlantic Division.
"A big part of this game is playing with some confidence and that's what I'm doing right now," Callahan said.
"We just seem to be able to find each other. We know where we're going and we've played together now for a bunch of games and we're getting used to each other and things are clicking."
Rangers goalie Henrik Lundqvist recorded 33 saves to aid in the victory.
(Reporting by Jahmal Corner in Los Angeles; Editing by Edited by Patrick Johnston)