The Stars were outshooting the Devils 27-2 at 7:52 of the second period, but New Jersey, which went 23:42 without a shot on goal, from 5:16 of the first to 8:58 of the second, took a 1-0 lead 3:41 into the game when Palmieri tapped in a pass from Andy Greene.
"First half of the game wasn't good, and we all knew that," said Palmieri, who has scored at least 20 goals in four straight seasons for New Jersey, including an NHL career-high 30 in 2015-16. "Blackwood made some saves that kept us in it. I don't think you can play the way we did and expect to have a great opportunity to win a game, especially on the road. But we had a shot."
Benn scored from the top of the crease off a pass from below the goal line by Radulov to tie the game 1-1 at 12:31 of the first.
The goal ended Blackwood's shutout streak at 135:26. The five goals are the most he has allowed in five NHL starts since being recalled from Binghamton of the American Hockey League on Dec. 18, after Cory Schneider sustained an abdominal strain.
"I knew I wasn't going to get a shutout every game," said Blackwood, who made 25 saves in a 4-0 win against the Vancouver Canucks on Monday and 37 in a 2-0 victory against the Carolina Hurricanes on Dec. 29. "I definitely did not expect to have as good a first couple of games as I did. It was kind of nice to have that, but you know it's a little bit of reality here."
Heiskanen gave Dallas a 2-1 lead at 3:21 of the second when he skated in alone from the point at 4-on-4 and deked Blackwood.