"(Dwight King) did all the work," Brown said. "He forced a turnover. (Mike Richards) picked up the loose puck, and (Richards) is one of those guys that kind of looks to pass first. I thought it was just coming late. My shot was just to get it by the D and on the net."
The victory allowed Los Angeles, the defending Stanley Cup champion, to salvage the final game of a 1-3-1 road trip.
Dallas is 0-3-2 in the last five games, and 1-1-4 at home this season.
To Stars coach Lindy Ruff, Brown's goal from the slot at 4:23 and Clifford's deflection at 11:35 were the result of Dallas giveaways.
"When I look at the sheet and I see 19 giveaways, we're not going to win hockey games," Ruff said. "That's where I have to change the mentality. That's my job. Enough of the pond hockey. Enough of open plays."
Trevor Lewis' shot from the left faceoff circle went in off Clifford's skate in front of Lehtonen.
"There's some things I need to clean up a little bit," Quick said. "We were able to win the third period on the road, so that's (good), especially against a team as good as Dallas. We can take that momentum and carry it back home."
Quick finished with 33 saves. Lehtonen had 27 before being pulled for an extra skater with 1:58 left.
Lewis tied the game at 1 with a short-handed goal 2:55 into the second period. It was Los Angeles' NHL-leading fourth short-handed goal, and third on the current trip.
In the first four games of the trip, the Kings scored only six goals and were 1 for 11 on power plays.
Dallas had been outscored 17-10 in its previous four games, and failed on all 10 power plays in the last two.
The Kings were 0 for 5 on the power play Tuesday, and failed to score on a 5-on-3 advantage for 1:06. Dallas was 0 for 4.
On the Stars' goal, Jordie Benn passed from the Dallas zone to Vernon Fiddler at the opposite blue line. Fiddler then fed Horcoff as he skated between two defenders down the slot and put the puck past Quick.
"It was just a great play, a great pass by (Fiddler)," Horcoff said. "He came to my side. I kind of broke to the middle. Benn gave him a great outlet."
Los Angeles outshot the Stars 12-9 in the first when the Kings failed to score on two power plays. In the second, Lewis outmaneuvered Benn for the puck, and shot past Lehtonen.
NOTES: C Tyler Toffoli scored the Kings' first three short-handed goals. . Richards has at least one point in all 10 games he has played in Dallas (3 goals, 11 assists). . D Sergei Gonchar (fractured ankle) and RW Valeri Nichushkin (lower-body injury) both returned to Dallas' lineup. Gonchar had not played this season and Nichushkin had been out since Oct. 11. Nichushkin returned to a line with Jamie Benn and Tyler Seguin. Jason Spezza skated with Ales Hemsky and Erik Cole. . D Trevor Daley played in his 700th NHL game, all with the Stars.