The Rapids extended their home unbeaten streak to five games and, with a 9-6-10 record, moved within a point of third-place Seattle in the Western Conference.
Mullan scored in the 54th minute, firing a shot that sailed just below the crossbar.
Columbus (9-7-7) missed a chance to open some distance over second-place Philadelphia in the Eastern Conference. Philadelphia could move into a tie for the conference lead with a win Saturday.
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