The Rangers eliminated the Devils in five games to become the second team from the East to advance past the first round of the NHL playoffs. Pittsburgh completed a series sweep of Ottawa earlier in the week.
Henrik Lundqvist made 23 saves for New York.
New Jersey was eliminated in the opening round for the first time in four years.
The Rangers overcame an early 1-0 deficit with three goals in the first period. Rozsival scored 4:58 into the game to tie it, and less than two minutes later Jagr put New York in front to stay with a power-play goal.
New York boosted its lead to 4-1 before the Devils clawed back to within one. Dubinsky ended all doubt, however, with an empty-net goal in the game's final minute.