Dax McCarty, near midfield, first-timed an arcing pass to a charging Katai, who took a couple dribbles and then fired a low cross to Sapong for a sliding empty-net finish inside the back post from point-blank range to give the Fire (2-2-3) a 2-1 lead in the 53rd minute.
Chicago's Nemanja Nikolic, at the top of the 6-yard box, headed home a high entry by Nicolás Gaitán to make it 1-0 in the 34th before Kei Kamara scored , for the fourth consecutive game, to tie it at 1-all in 40th minute.
Gaitán flicked a short cross to Djordje Mihailovic, a 20-year-old homegrown, for a tap-in goal in the 61st and Katai, on the left side, cut back to evade a defender and then rifled a bending shot inside the far post from outside the area in the 81st.
Colorado's Jack Price, after video review, was shown a red card in the 86th minute.
The Rapids (0-6-2) are winless since beating FC Dallas 2-1 to close the 2018 MLS regular season.
Chicago is unbeaten in four straight.