Jagr, playing in his 19th NHL season, had his first multi-goal game since the opening night of the season Jan. 19.
He began the scoring with a power-play goal 5:28 into the contest and then delivered the second of the three goals Dallas used in the final period to break open the game.
The Stars won their second in a row and jumped from last place into a tie for second in the tightly packed Pacific Division.
Los Angeles took a 2-1 lead with 4:30 to play in the second period, but could not put another shot past Kari Lehtonen.
Cody Eakin tied it on the power play with 1:14 left in the second and Dallas then dominated the third period. Brenden Morrow gave the Stars the lead 5:16 into the stanza, Jagr scored his ninth of the season midway through and Antoine Roussel added an empty-net goal with 1:41 to play.
The Kings had won two in a row and seven out of eight.
Lehtonen stopped 31 shots while Jamie Quick surrendered four goals on just 21 shots.