Lundqvist turned aside all 28 Carolina shots during the first two periods, giving the Rangers a chance to grab a commanding lead with three goals in the middle frame.
Derek Stepan, Rick Nash (a goal and an assist each) and Ryan Callahan each scored during the big period for New York, which extended its lead over New Jersey for the eighth and final Eastern Conference playoff seed to three points.
Brad Boyes added an empty-netter for the Rangers.
Zac Dalpe scored for fading Carolina, which dropped a fourth straight.
Dan Ellis started in net and was pulled late in the second period after allowing three goals on 30 shots.
Justin Peters made eight saves the rest of the way.
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