After New York squandered three one-goal leads, Nedved came through with his second of the night to put the Rangers ahead for good.
Moments after coming off the bench, former Lightning Matthew Barnaby sent the puck between the legs of Tampa Bay defenseman Dan Boyle. Nedved picked it up in the right faceoff circle and put a backhander between goaltender Nikolai Khabibulin's pads.
Pavel Bure capped a two-goal night with an empty-netter in the final minute, sealing the win.
New York has recorded back-to-back wins for the first time since Feb. 8-10 but still trails Montreal by five points for the final playoff spot in the Eastern Conference with five games remaining.
Rookie Dan Blackburn made 26 saves and Rem Murray and Martin Rucinsky also scored for the Rangers, who squared the season series at two wins apiece.
Vaclav Prospal had a goal and an assist but could not prevent the Lightning from suffering their fourth straight loss.