Halpern's first goal of season came when he rebounded Jere Lehtinen's shot past Los Angeles goalie Mathieu Garon.
The Stars, who lost Friday night to Detroit, extended the Kings' winless streak to five games (0-4-1). It is the longest slide for Los Angeles since it lost the last 11 games of the 2003-2004 season.
Smith, who shut out the Phoenix Coyotes in his NHL debut on Oct. 21, improved to 2-0 as starter Marty Turco took the night off.
Los Angeles continued to struggle offensively as it has scored just 14 goals over the last 10 games.
Philippe Boucher and Stu Barnes had goals as Dallas, 9-2-0, matched the franchise mark that was set in 1996-97.
Barnes' first goal of the season gave the Stars a 2-1 lead with 44.5 seconds left in the second. Rob Blake scored early in the second on a power play, snapping the Kings' 0-for-23 slide with the man advantage.
The Kings tied the score at 2 on Tom Kostopoulos' goal at 7:10 of the third.
Los Angeles pulled Garon in the final minute and had a two-man advantage for the final 28.7 seconds when Sergei Zubov was called for hooking. However, the Kings couldn't get a shot off.
Garon had 25 saves for Los Angeles, but he was bested by the 24-year-old Smith.
Smith, who faced 22 shots against the Coyotes, but saw far more action from the Kings. Los Angeles outshot Dallas 34-28 one night after taking 38 shots in a 2-0 loss to Columbus.
Los Angeles, who came in next-to-last on the power play, was 1-of-8 with a man advantage.
Boucher opened the scoring with a goal from just above the right circle at 14:34 of the first.
Blake flipped a shot from near the blue line for his first goal of the season, and Los Angeles' first power-play goal in five games.
Dallas' Matthew Barnaby had two assists, including a nice pass to a streaking Barnes, who beat Garon from the right circle to give the Stars a 2-1 lead with 44.5 seconds left in the second.
Notes: Dallas C Steve Ott left the game in the second and did not return because of an ankle injury. ... Los Angeles C Craig Conroy played in his 700th NHL game. ... Dallas C Mike Modano saw his four-game goal streak end.