The Kings took a 1-0 lead at 18:04 of the first period three seconds into a power play. Brown, just outside the crease, redirected a wrist shot from the left point by Drew Doughty following a face-off win by Anze Kopitar.
It was the first power-play goal for the Kings in six games. They had the worst road power play in the NHL (10 percent; 5-for-50).
"Tonight we decided to simplify it," Doughty said, "try to get a puck at the net the first five to 10 seconds of the power play."
Hagelin gave Los Angeles a 2-0 lead at 4:39 of the second period with his second goal of the season and his first since being acquired from the Pittsburgh Penguins on Nov. 14 in a trade for Tanner Pearson. Bishop made a save at the near post on a shot by Tyler Toffoli but failed to control the puck. Hagelin, skating across the crease, tapped in the rebound on the opposite side.
Hagelin has played six games since missing 20 with a lower-body injury.
"He battled for it, came back from injury, and things haven't gone quite as well for him since he's been back," Kings coach Willie Desjardins said, "so it was nice to see him get one."
Hagelin said, "You're always trying to contribute offensively as much as you can. We've had our looks. I've had my looks. It's nice to finally see one go in."
Dallas, with an extra attacker, ended Campbell's shutout with 1:04 left on a deflection by Lindell. It ended a 14-game goal drought dating to Dec. 15.
Stars forward Alexander Radulov, second on Dallas with 39 points and third with 14 goals, was benched by coach Jim Montgomery for the second half of the first period.
"I wasn't playing good. I talked back to Coach, and he basically sat me until the end of the period," Radulov said. "It's the right decision. I can't do that. It's been an issue in my career, but I'm going to learn from it. I'm going to be better, try to not make those mistakes again."
Montgomery said, "Every decision we make is what's best for the Dallas Stars. And at that moment, I thought that was best for the Dallas Stars. … When you're struggling to score goals, it (the benching) is hard to do with a player of that caliber."
Dallas' past three losses have been at home, with their next three games also at home.
"It's a wasted opportunity is what it is," Montgomery said.
