They were the only victors with the other three matches, between Comoros and Gambia, Libya and Rwanda and Tanzania and Ethiopia, all drawn.
Fighting between the national army and a paramilitary force in Sudan erupted in April 2023, forcing the national team to train and play abroad since.
Sudan hosted Niger in Juba, capital of neighbouring South Sudan, and a 51st-minute goal from Thailand-based Abo Eisa secured maximum Group F points.
Comoros were another country that could not play at home because there is no international-standard stadium in the country.
They hosted Gambia in the Moroccan Atlantic city of El Jadida and broke the Group A deadlock on 37 minutes through Youssouf M'Changama.
Saudi Pro League midfielder Musa Barrow levelled in first-half added time for the Gambians, and there were no further goals.
The Group D opener between Libya and Rwanda in Tripoli also finished 1-1 with Subhi al Dhawi netting after 17 minutes and Innocent Nshuli equalising two minutes into the second half.
Ethiopia did not manage one shot on target as they drew 0-0 with Tanzania in Group H in Dar es Salaam.
There are seven qualifiers scheduled for Thursday with four former African champions - Algeria, Congo Brazzaville, Ghana and Tunisia - among the nations in action.
