Butler scored 17 of his points in the first quarter and went 6-for-6 from 3-point range as the Clippers finished December at 16-0 -- only the third team in NBA history to post such a mark in a single month.
The Clippers' streak started with a Nov. 28 win over Minnesota.
Chris Paul scored 19 points, distributed nine assists and made five steals for Los Angeles, which extended its franchise-record winning streak and improved to an NBA-best 25-6 on the season.
Jamal Crawford added 19 points off the bench for the Clippers.
Al Jefferson led the Jazz with 30 points, eight rebounds and four blocked shots.