The only goal of the game was scored by United States international Chris Wondolowski, who found the net with just over 20 minutes remaining at Buck Shaw Stadium.
It takes Mark Watson's side to sixth in the MLS Western Conference, one point behind the Rapids.
The Quakes were the better team for most of the evening, although they had to wait until the 69th minute before Wondolowski headed home to opening goal from a Shea Salinas corner kick.
It was an eighth assist of the season for the 27-year-old from Texas, which is a new club record.
Rapids goalkeeper Clinton Irwin had to be on top form to prevent him from making it nine for the season as Alan Gordon threatened to put the hosts out of sight by converting another corner in the 82nd minute.