Sudan's first victory at the Africa Cup of Nations in 42 years has allowed them to qualify for the quarter-finals of the competition.
Haitham Mustafa's side were largely unfavoured heading into this encounter, but two goals from Mohamed Tahir sealed their progression.
Tahir's first of the evening came after 32 minutes when he beat the Faso offside trap to slot the ball past an advancing Daouda Diakite in goal.
His second took until the 82nd minute arrive and it came courtesy of a mistake from Diakite. The Faso goalkeeper hesitated inside his area and Tahir capitalised to roll the ball into an empty net.
Faso claimed a late goal courtesy of Moumouna Dagano but it proved to be little more than consolation.
Sudan will now play Zambia in the next round.