Jiri Tlusty and Jordan Staal set up each other for goals in the second period as the Canes took a 2-1 lead.
Staal passed to Tlusty in the low slot for a score 33 seconds into the second as the Canes grabbed the lead. Defenseman Kevin Klein tied it 1-1 for the Rangers at 4:22 of the period, but Tlusty and Staal teamed up again with 1:42 left in the second.
Staal beat Rangers defenseman Anton Stralman to the puck along the right boards in the Rangers zone, then passed across ice to Tlusty. Staal broke in, took the pass from Tlusty and easily beat goalie Henrik Lundqvist.
Tlusty's goal was his 11th and Staal's his 13th. Andrej Sekera and Alex Semin also had assists on the two Canes goals.
Klein scored his first goal as a Ranger and his second of the season when the Rangers caught the Canes in a line change. Klein was unchecked between the circles and ripped a shot high to the glove side on Canes goalie Cam Ward.
Ward earned the start after relieving Anton Khudobin in the Canes' 5-4 loss Saturday at New Jersey.
The Canes weren't lacking energy in a scoreless first period against the Rangers, getting to loose pucks, winning board battles and building a 13-5 shooting edge.
The Rangers were penalized just 16 seconds into the game -- Stralman for hooking Jordan Staal -- but the Canes couldn't jump to an early lead. Both teams had a pair of power plays in the first.
Ward faced just five shots in the first but had to make a some sharp saves. Two came on shots by Martin St. Louis, who crashed the net about 10 minutes into the period for an attempt, then got off a shot late in a Rangers power play.
St. Louis' second shot came after the Rangers' Benoit Pouliot collided with Canes defensemen Ron Hainsey and Mike Komisarek near the Carolina blue line, causing both to fall.
The Rangers' Derick Brassard tested Ward about three and a half minutes into the first, but Ward made a quick move out of net to his right to make the stop.
A quick skirmish broke out midway through the first when the Rangers' Ryan McDonagh made a high hit on Tlusty in the neutral zone. McDonagh was penalized for interference and roughing, and the Canes' Brett Bellemore for roughing after jumping into the fray.
The Canes and Rangers played on Friday at PNC Arena, with the Rangers using a late surge for a 4-2 victory, their 10th straight over Carolina.