Landon Donovan, Baggio Husidic and Gyasi Zardes netted braces in the resounding win on an emotional night at the StubHub Center.
It came after Rapids goalkeeper Joe Nasco was shown a red card in the opening minute in California.
The win was the Galaxy's fifth straight and saw them close to within two points of Western Conference leaders the Seattle Sounders.
For the Rapids, it marked their seventh straight loss and left them in that position in the table.
The Galaxy paid tribute to defender AJ DeLaGarza's son Luca, who died on Thursday a week after being born following a fight with the complications of hypoplastic left heart syndrome.
Already out of form, the Rapids made the worst possible start away from home inside 40 seconds.
Nasco was sent off after pulling down Alan Gordon, who looked set to open the scoring.
Instead, Donovan made it 1-0 as he gave substitute shot-stopper Clinton Irwin no chance with his penalty.
It was 2-0 in the 29th minute as Husidic finished off a team move by placing an effort into the bottom corner.
Donovan set up Zardes to triple the lead on the stroke of half-time.
They changed roles straight after the break as Zardes was brought down inside the area and Donovan stepped up to put away another penalty.
Zardes headed in a fifth before Donovan set up another goal, this time for Husidic to complete the rout.
