King made a career-high six 3-pointers for the Buffaloes (11-7, 3-3), who earned their first road win of the season. The team's lone starting senior finished one point short of his career high while grabbing 10 rebounds.
Thomas Welsh scored 20 points - two off his career best - to lead the Bruins (13-5, 4-2).
King scored eight in a row, including consecutive 3-pointers, to push Colorado's lead to 55-41.
Welsh took over for UCLA, scoring 10 in a row to close to 55-51. The 7-footer made two 3-pointers while teammate Chris Smith missed three free throws.
Most of the other Bruins were no better at the line, where the team was 8 of 18, a statistic surely galling to coach Steve Alford, who was a top foul shooter at Indiana.
King answered with his sixth 3-pointer and Colorado led 60-51. It was part of a 13-8 run the Buffs used to close out the game.
After falling behind by 17, the Bruins closed the first half with a 12-5 run, including nine in a row, to trail 39-29 at the break. Four different players scored for UCLA, with Aaron Holiday contributing five straight. The Bruins shot 36 percent from the floor and made just 2 of 11 3-pointers in the half.
Colorado: The Buffs were 0-6 on the road, but the win got them back to .500. Defensively, they limited UCLA to 37 percent shooting from the floor and forced Holiday - UCLA's best defender - into six of the Bruins' 10 turnovers.
UCLA: The Bruins had their two-game winning streak snapped by losing to a team they had owned since the Buffs joined the league in 2011-12. UCLA is 11-3 all-time against the Buffs, and had won seven of eight coming in. A win would have given the Bruins sole possession of first place in the league after No. 17 Arizona won earlier.
Colorado: Hosts Washington State on Thursday.
UCLA: Visits Oregon State on Thursday.
For more AP college basketball coverage: http://collegebasketball.ap.org and http://twitter.com/AP-Top25