The Devils' winning streak came after a season-high, four-game losing streak.
New Jersey, which has played inconsistently on the road while going nearly unbeaten at home (11-1-1), had lost four straight away from Continental Airlines Arena. The Devils improved to 6-8-1 on the road.
Eric Rasmussen, Patrik Elias and Sergei Brylin scored third-period goals for the Devils after the Bruins cut their deficit to 2-1.
Marc Savard had the goal for Boston, which lost for just the fourth time in 14 games.
Boston goaltender Tim Thomas, playing in his 21st straight game, was lifted at the start of the second period in favour of Hannu Toivonen.
The Devils outshot the Bruins 42-20.