Quick, who stopped 28 Dallas shots, became the first goalie in Kings history to notch three straight shutouts. He also blanked the St. Louis Blues and Phoenix Coyotes this week.
Quick set another Kings mark as well by not allowing a goal in 188 minutes, 10 seconds, besting a record held by Rogie Vachon.
Jack Johnson of Los Angeles tallied the game's only goal with 4:58 remaining in the contest.
The Stars' Andrew Raycroft got the hard-luck loss, turning aside 23-of-24 shots.