The victory lifted the multi-island nation of less than 900,000 inhabitants off the south east coast of Africa two places to second in Group I, one point behind leaders Ghana.
The nine group winners in Africa qualify for the 2026 World Cup in the United States, Canada and Mexico, and the best four runners-up get a second chance in play-offs.
Comoros are currently the fourth best second-placed team with 15 points, behind Cameroon and Senegal only on goal difference.
Captain Youssouf M'Changama and Myziane Maolida, both born in France to Comoran parents, scored after 20 and 39 minutes to give the islanders a fifth victory in eight qualifiers.
The match was played in the Moroccan city of Meknes because the Central African Republic does not have a FIFA-approved stadium.