"I was waiting for this one for awhile," Danis said. "I was nervous before the game, but it's definitely good to get the first one out of the way."
Zubrus scored off a rebound of Jamie Langenbrunner's shot.
Zach Parise also assisted on Zubrus' goal and has 10 points in the last six games for New Jersey, 6-0 on the road and 1-4 at home.
"No idea how we find ways to win, just find a way that is good," Devils coach Jacques Lemaire said.
Tim Thomas made 29 saves for Boston, 3-4 on home ice.
"I was pretty sure I didn't have the first one," Thomas said. "The second one I thought maybe I did for a second and by the time I could check, there was nothing I could do."
David Clarkson opened the scoring for the Devils at 13:25 of the first period.
The Bruins failed to record a point for only the second time in the last six games.
"We are never happy with losing games," Bruins defenseman Derek Morris said. "It was one bounce that went the wrong way, but I thought we had a hard effort tonight."
Boston had a pair of opportunities in the final 1:26, including a shot that beat Danis but clanked off the crossbar.
The Devils bounced back after losing to Buffalo 4-1 on Wednesday night, They will finish their trip at Tampa Bay before returning home to face Washington.
Boston will host Edmonton on Saturday night.
- Boston was 0 for-2 on the power play and is 6 for 42 overall.
- Devils rookie Niclas Bergfors assisted on Clarkson's goal and has four points in the last four games.
- Marco Sturm and Zdeno Chara had assists for Boston.