The Kings snapped a three-game losing streak and moved into a ninth-place tie with San Jose, three points behind eighth-place Edmonton in the Western Conference. The Sharks lost at home in overtime to Phoenix.
"It's like a playoff atmosphere here, if we don't win games it's sayonara for us and nobody in here wants that," said Roenick, who ended a 10-game goal-scoring drought with the game winner. "Tonight's the way we have to play -- we have to play defensively and dig games out."
Roenick swiped in Sean Avery's pass from behind the net to give the Kings a 1-0 lead 10:21 into the game.
Acquired from Philadelphia last summer, Roenick matched his career-low with his ninth goal. He has 19 points in 51 games this season, just topping his 18-point total in 20 games as a rookie with Chicago in 1988-89.
"Hedberg was excellent in goal and gave us a chance to win, but we couldn't come up with the goal that we needed to get back in the game," Dallas coach Dave Tippett said.
The Kings won six of the eight-game season series between the teams.
"We've been disappointed by the Kings all year, they have our number," Stars forward Brenden Morrow said. "We had some of our key players out of the lineup today, but we still wanted to come out with a good effort. We had a lot of fight in us, but couldn't come up with the goals we needed."
Garon stopped Jussi Jokinen on a breakaway in the second period and moved out of his crease to stuff Morrow on a point-blank shot minutes later.
In the third period, Garon needed to kicked out a shot by Jokinen from the left circle during a Dallas power play to earn his third shutout of the season.
Los Angeles had a four-point lead over Dallas atop the Pacific Division on Jan. 2, but the Stars have been 23 points better than the Kings since then.
Part of the Kings' problems have stemmed from Roenick's lack of production.
"It's going to take certain individuals (to step up) every night as a team to win," said interim head coach John Torchetti who improved to 2-3 in since replacing Andy Murray on March 21. "I know we have a short amount of time, but we have to strengthen as a team."
- C Derek Armstrong and D Aaron Miller were both out of Los Angeles' lineup with back injuries. C Eric Belanger was held out with concussion-like symptoms.
- Dallas D Sergei Zubov missed a second game with a lower-body injury.