Leader of the Western Conference, LAFC had its 10-match unbeaten streak in all competitions ended with a 1-0 loss to the struggling Rapids in Denver.
The game's only goal came four minutes into the second half, former Liverpool and Rangers defender Danny Wilson heading in a Jack Price corner at Dick's Sporting Goods Park.
After a delay because of lightning, Colorado closed out its win, moving off the bottom of the Western Conference, which LAFC tops by six points.
In the day's other game, the Red Bulls claimed a 3-1 victory over Chicago Fire in New Jersey.
Alejandro Romero opened the scoring in the eighth minute, dispossessing goalkeeper Kenneth Kronholm before tapping into an open goal.
Brian White tucked away a Daniel Royer cross to double the Red Bulls' lead just before the hour-mark, only for Nemanja Nikolic to pull a goal back for Chicago.
However, Royer sealed the hosts' win after a Kyle Duncan cross as the Red Bulls moved into fourth in the Eastern Conference, while Chicago is eighth.