Lundqvist has the NHL lead in shutouts this season with eight. He was on track to pick up his ninth before Sergei Gonchar scored on the power-play 4:56 into the third.
By that time the Rangers had taken command with four unanswered goals, including two that came just 12 seconds apart in the middle period from Mats Zuccarello and Artem Anisimov.
Vaclav Prospal opened the scoring with a slap shot midway through the first period and Derek Stepan added his 18th of the season 2:25 into the third.
New York halted a three-game losing streak, having begun the evening a point behind Carolina in eighth place in the Eastern Conference. The Rangers increased their lead over ninth-place Buffalo to four points, although the Sabres have four games in hand against New York.
Craig Anderson allowed all four goals on 27 shots.