New Jersey overcame a 2-1 deficit to grab home-ice advantage in the Eastern Conference Finals. With the series deadlocked at a game each, the Devils will host the next two contests Saturday and Monday.
Martin Brodeur made 23 saves to record the 108th post-season victory of his career. He stopped all eight shots he faced in the final period.
New Jersey's Ryan Carter tipped in a shot with just 1:51 remaining in the second period to forge a 2-2 tie and Clarkson also scored on a tip-in 2:31 into the final stanza.
Ilya Kovalchuk opened the scoring for the Devils with a power-play goal 13:39 into the contest and New York then tallied twice in the second to take a brief lead.
Marc Staal beat Brodeur with a slap shot 2:23 into the second and Chris Kreider scored on the power play with 7:41 to go in the middle period.
Henrik Lundqvist was unable to protect the lead for the Rangers, allowing three goals on 27 shots.
Five of New Jersey's nine playoff victories this season have come by one goal.