Trevor Daley added a goal, and Mike Ribeiro had two assists for Dallas. Michael Cammalleri had a power-play goal for Los Angeles.
Dallas is 6-0 against Los Angeles this season, outscoring the Kings, 23-11. Los Angeles has lost four straight overall.
Barry Brust, playing in his ninth NHL game, made 22 saves for the Kings. Los Angeles is without its top two goalies, Mathieu Garon (finger) and Dan Cloutier (hip).
Coach Marc Crawford picked Brust over rookie Yutaka Fukufuji, who became the first Japanese-born player to play in an NHL game when he came on in relief of Brust in a 6-5 loss at St. Louis on Saturday.
Stars centre Jeff Halpern was a late scratch after sustaining a lower-body injury in warmups, and defenceman Philippe Boucher did not return to the ice after the first period because of an undisclosed injury.
Dallas remained without five other regulars, including top offensive threat Mike Modano, who missed his 19th consecutive game with a hip/groin injury.
Also out for the Stars were defenceman Sergei Zubov (elbow) and forwards Brenden Morrow (wrist), Steve Ott (ankle) and Matthew Barnaby (concussion).
Dallas scored its 10th power-play goal in 31 chances against Los Angeles this season when Barnes connected for his sixth goal of the season on a close-range backhander at 16:01 of the opening period.
Hagman made it 2-0 on Dallas' second power play, converting Jussi Jokinen's setup at 8:00 of the second period for Hagman's 10th goal of the season.
Cammalleri cut the deficit to 2-1 at 9:43 of the second period with his 18th goal of the season. But Daley's goal from the slot at 6:56 of the final period - Daley's second of the season and sixth of his career - extended Dallas' lead to 3-1.
Notes: Dallas has outscored Los Angeles 11-0 in the first period this season. . . . The Stars were playing a rare matinee to commemorate Martin Luther King Day. The crowd was announced at 17,992, but there were plenty of empty seats as fans stayed home because of icy driving conditions. . . . Hagman matched his career high for goals. . . . Barnes has three goals and two assists against the Kings this season.