Tuukka Rask made 20 saves, Patrice Bergeron had a goal and an assist, and Brad Marchand had two assists for the Bruins (31-14-6), who have won four straight and 10 of their past 12 games.
Boston moved one point ahead of the New York Islanders, who lost 4-2 to the Buffalo Sabres on Monday, for third place in the division.
"This is a great accomplishment. It's definitely not easy," Rask said. "You look at our division, it's tough, there's no room to have slumps. You've got to be able to keep up with other teams. We've had our ups and downs, but I think lately we've kind of found our game and our identity and kind of stuck to it."
Scott Wedgewood made 39 saves for the Devils (17-28-7), who had their four-game point streak end.
"They put the pressure on early and kept us under for the first 10-15 minutes," Wedgewood said. "That's a strong team with a strong push early. We were back on our heels and we're trying to tilt the ice the other way for the rest of the game.
"They obviously had a goal (of clinching a playoff berth) and they were attacking it."
Rask stopped Janne Kuokkanen on a 2-on-1 at 5:02 of the second period to keep it 0-0.
"It's always a challenge, physically and mentally, but I think we've got to be proud how our team handled this past month when we're playing every other night or back-to-back situations," Rask said. "The physical aspect has been the most challenging for me.
"Every game is different, and with experience and age, you kind of see a lot of things happen. You don't need more or less shots ... you kind of take them as they come."
Nick Ritchie gave the Bruins a 1-0 lead at 9:08 of the second on a one-timer from low in the right face-off circle after receiving a diagonal cross-ice pass from Jakub Zboril.
"They were clicking with every line," Devils coach Lindy Ruff said. "They were winning face-offs, they had puck possession. I think their speed exposed us a little bit; our gaps weren't good. We couldn't take enough ice away from them."
