The Kings (37-20-4) won their fourth straight and have scored two goals in each game of the streak. They are four points ahead of the Anaheim Ducks in the race for first place in Pacific Division. The teams play Sunday at Honda Center.
The Sabres (25-31-7) went 1-2-0 on a three-game California trip.
Enroth, who played for the Sabres from 2009-10 to 2014-15, earned his seventh career shutout and first win since Jan. 24.
"It means a lot, even though my feelings for them kind of fade away," said Enroth, who was traded by Buffalo to the Dallas Stars on Feb. 15, 2015, and signed with the Kings last summer as a free agent. "It's been a while since I played for them. Definitely feels good to beat your old team, especially to get a shutout. I'm going to try to build on this and try to make this something positive."