Campbell made 18 saves in the third period, when Los Angeles was outshot 19-3. Dallas selected Campbell at No. 11 in the 2010 NHL Draft and he played one game for the Stars before being traded to the Kings on June 25, 2016 for defenseman Nick Ebert.
"I'm pretty sure everyone in the hockey world knows my story, how it didn't work out here," the 27-year-old said. "Nothing more I wanted at 18 (years old) or 19, 20, 21, 22 is to be the franchise goalie here. Didn't happen, but it's great to come back here."
[WATCH: All Kings vs. Stars highlights]
Dustin Brown and Carl Hagelin scored for the Kings (19-25-4), who have a three-game point streak (2-0-1).
Esa Lindell scored for the Stars (23-21-4), who have scored three goals losing four straight games, which matches their longest losing streak of the season (Dec. 9-15). Ben Bishop made 17 saves.
"We're all looking for the pretty play until that third period there, and we started simplifying and getting deep and going to hard areas," Dallas forward Tyler Seguin said. "We were better in the third, but we've got to be more dirty on that."
Video: LAK@DAL: Brown redirects Doughty's shot for PPG
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.
Video: LAK@DAL: Hagelin chips in rebound from doorstep
They said it
"I backed up a few times here. It kind of allowed me to settle in a little bit before I played my first game." -- Kings goalie Jack Campbell on his first game played at American Airlines Center
"We had tons of chances in the third, so we've learned our lesson and realized that's how we have to play from the start of the game to the finish." -- Stars forward Blake Comeau
Need to know
Los Angeles, which went into play with the fewest points in the NHL, is 7-0-0 when leading after the first period. ... Doughty's assist was his first point in five games. ... It was the first loss for Dallas against a Pacific Division opponent in nine games. ... Stars forward Tyler Pitlick left during the third period with an upper-body injury. ... Seguin leads Dallas with 43 points and is second with 17 goals; Jamie Benn has 18 goals.
Kings: At the Colorado Avalanche on Saturday (3 p.m. ET; ALT, FS-W, NHL.TV)
Stars: Host the Winnipeg Jets on Saturday (7 p.m. ET; SN360, SNW, SNP, FS-SW+, NHL.TV)
Video: Hagelin, Campbell pace Kings past Stars, 2-1