The disciplinary committee of football’s world governing body ruled that Saif Ali should not have played in the June 2 game in Khartoum.
Zambia protested that Ali played despite receiving yellow cards in previous competitive matches, including when Zambia beat Sudan in an African Cup of Nations quarter-final in February.
Fifa declared the match “lost by forfeit by Sudan,” awarding Zambia a 3-0 victory and with it the three points for a win.
The Sudan football association has also been fined US$6,430.
Zambia now leads Group D with six points from two matches, and Sudan falls to third place with one point.
Ghana are in second place with three points while Lesotho are bottom with a single point.