Modano scored his 14th of the season and third in five games on a quick shot from the high slot, beating Sean Burke to move three goals behind Joe Mullen for the career lead among U.S.-born players.
Niklas Hagman and Trevor Daley added goals, and Marty Turco stopped 18 shots for the Stars, 1-2-2 in their previous five games.
The Stars have won all seven meetings with the Kings this season and are 19-7 against Pacific Division teams.
Ladislav Nagy scored a first-period goal to help Dallas improve to 85 points, two better than the San Jose Sharks for second spot in the division.
Dustin Brown scored two goals, Brian Willsie added a goal, and Burke made 30 saves for the Kings, 0-2-3 in their last five games.