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The Black Stars had held Sudan until the hosts finally got the breakthrough on the brink of the 90 minutes of regulation time.
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The hosts dominated the greater part of the first half, but they fluffed the opportunities that came their way in the first half.
In the 30th minute, Fatau Dauda came to the rescue of the Black Stars when he made a point-blank save to deny the Birds of Sudan from breaking the deadlock.
Ghana also came into the game when Mubarak Wakaso put Tariqe Fosu through, yet the latter was closed in by the Sudanese goalkeeper.
Back from recess, the Black Stars started from where they left off and continued to dominate play.
Jordan Ayew tested the goalkeeper, but he stood to the test to save the situation.
The likes of Caleb Ekuban, Samuel Owusu also made incursions in the opponents’ goal area, but they were denied from finding the back of the net.
The tide getting to the end of the game tilted in favour of the hosts and they threw everything into the game.
However, John Boye in one of those moments for the hosts cleared his lines to stop the Sudanese from breaching the defence line.
And Fatau Dauda also made a good save to put the game goalless.
CK Akonnor, brought on Christopher Nettey to strengthen his defence in the late minute, but the North Africans continued to pin Ghana to the wall and finally got the breakthrough in the 90th minute when Mohamed Rahman slotted home the much-needed goal.
Ghana defeated Sudan 2-0 last week Thursday t take their points tally to 9 points.
The West Africans would have booked their ticket to the 2022 Africa Cup of Nations with two matches to spare if they had held Sudan to a draw on Tuesday.
Starting line-up:
Fatau Dauda, Nicholas Opoku, Abdul Baba Rahman, Alexander Djiku, John Boye, Afriyie Acquah, Mubarak Wakaso, Tariqe Fosu, Jordan Ayew, Caleb Ekuban, Jefferey Schlupp.
Reserves: Clifford Aboagye, Emmanuel Lomotey, Majeed Ashimeru, Ati Zigi Lawrence, Kwadwo Amoako, Joseph Aidoo, Samuel Owusu, Christopher Nettey, John Antwi