During a power play, Lindros - who had just two goals in his first 19 games - grabbed the puck among three Carolina players at the edge of the left faceoff circle and surprised goaltender Kevin Weekes with a quick shot at 1:41.
It was the second power-play goal of the night for the Rangers, who are ranked 28th in the NHL and had none in the previous six games.
Just 62 seconds later, defenseman Dale Purinton moved past Carolina's Erik Cole, used Lindros as a screen and fired a slap shot past Weekes from the left circle.
Ronald Petrovicky had tied it for New York with a power-play tally with 4:52 to go in the second period, banking the puck off Weekes' left skate from behind the net.
Defenseman Glen Wesley scored his first goal of the season for the Hurricanes, a point shot that deflected off Petrovicky and eluded Petrovicky.
Making his ninth straight start in place of the injured Mike Richter, Blackburn stopped 30 shots for his fifth win.