Wells Thompson and Sanna Nyassi each had an assist for the Rapids (9-6-10), who have won four of six. Matt Pickens got the shutout.
Thompson helped set up Mullan's first goal for Colorado in the 55th minute. Nyassi found Cummings in the 79th minute.
Eastern Conference-leading Columbus (9-7-7) was 3-1-1 in its last five Major League Soccer games. It next plays New England next Saturday.