Heber scored his team-leading eighth goal in the 40th minute and Sean Johnson made two saves for NYCFC (8-3-8, 32 points), which snapped a two-match losing streak and improved to 3-0-2 in five all-time matches versus Colorado.
Rapids midfielder Sebastian Anderson scored his first MLS goal in the sixth minute before seeing his night ended abruptly, courtesy of a red card. The 16-year-old Anderson was whistled for a dangerous foul on Ronald Matarrita.
Colorado goalkeeper Tim Howard finished with two saves before exiting with a strained right calf in stoppage time of the first half. Clint Irwin made five saves in relief for the Rapids (5-11-5, 20 points), who played without leading goal scorer Kei Kamara (back).
NYCFC dominated play against its short-handed foe before Colorado's Lalas Abubakar failed to clear the ball out of harm's way with a header in the 83rd minute. Mitrita settled the ball and unleashed a shot from outside the box that sailed inside the right post to give NYCFC a 2-1 lead.
Colorado wasted little time taking the early advantage as former NYCFC forward Jonathan Lewis raced up the left wing and into the penalty area before sliding a slick feed to the 16-year-old Anderson, who scored from close range.
Lewis was playing in his first match against NYCFC, which selected him with the No. 3 overall pick of the 2017 MLS SuperDraft.
Heber settled Maximiliano Moralez's entry pass with his chest before deftly unleashing a left-footed shot past Howard to forge a tie in the 40th minute. The goal was Heber's fourth in his last three appearances with NYCFC while the assist was Moralez's club-best 13th of the season.
NYCFC take advantage of extra man to beat Rapids
Colorado were reduced to 10 men when 16 year old Sebastian Anderson was sent off, opening the door for NYCFC to score twice and earn an away win.