Rapids substitute Andre Akpan was taken down during Colorado's desperate efforts to gain the equalizer with time running out and Omar Cummings was awarded a penalty shot.
But Saunders guessed correctly and made a diving stop on Cummings' shot, allowing Los Angeles (3-3-0) to hang on for its second straight win.
Colorado's Marvell Wynne scored an own-goal and Landon Donovan netted the go-ahead tally in the 39th minute for the Galaxy.
Cummings got the only goal for the Rapids (3-4-0).
Notable deaths of 2014 [PHOTOS]