The game was scoreless until the 50th minute, when Tony Cascio began a Rapids onslaught with a shot that reached the net through traffic.
Omar Cummings set up Hill for the first of his two goals in the 82nd minute as the Goats were pressing for the equalizer.
Jeff Larentowicz made it 3-0 on a penalty kick and Hill tallied again in stoppage time for the Rapids (4-4-0), who broke a three-match losing streak.
Chivas USA (3-5-0), meanwhile, lost its first road game of the season.
Celebrity Couples of 2014 [PHOTOS]