Connor Clifton scored, Brad Marchand had three assists and Tuukka Rask made 25 saves for Boston (13-3-5), which is 2-0-3 in its past five games.
David Krejci replaced Patrice Bergeron on the Bruins top line alongside Marchand and Pastrnak and had two assists. Bergeron missed his second straight game because of a lower-body injury.
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"It's always nice to get a chance to play with those two guys," Krejci said. "Those guys are two of the best players in the world, so they definitely make it easy on me."
The Marchand-Krejci-Pastrnak line totaled seven points (two goals, five assists).
Mackenzie Blackwood made 23 saves for New Jerseys (7-9-4), which was denied a third straight win.
"It's one thing if we had some bad bounces or ran into a hot goalie, but tonight was controllable mistakes, unforced errors and that's on us," Devils captain Andy Greene said. "It's about working hard with structure and playing the right way."
The Bruins are 8-1-0 in their past nine games against the Devils, including four straight wins at Prudential Center.
"I thought we played fairly stingy and when we had a chance to extend the lead on the power play, we simplified, got it to the net and took advantage of our opportunities," Boston coach Bruce Cassidy said. "I thought we did a good job limiting them."
Pastrnak, who leads the NHL with 19 goals, scored his second of the game off a slap shot from the right point on the power play to give the Bruins a 3-1 lead at 3:19 of the third period.