The Etienne Ndayiragije led-side dominated the proceedings with five shots on target compared to the visitors' two. Despite having a better junk of possession, the Taifa Stars were undone by the 61st-minute strike by Yassir Mohamed.
Good defending by the Zdravco Logarusic team ensured the hosts do not find an equaliser.
Sudan need a barren draw in the second leg at home to qualify for the tournament that will be held in Cameroon. The match will be played on October 18.
Tanzania eliminated Kenya in the previous preliminary round to advance while Sudan had been exempted from it.