Two first half goals from Asamoah Gyan and captain John Mensah deflated the hopes of Sudan who had promised fire and brimstone on the 2010 Fifa World Cup quarter-finals.
Striker Gyan tucked home the opener on sevenÂ minutesÂ when he profited from a goal-mouth melee.
The Nile Crocodiles piled on the pressure but the Black Stars well rehearsed counter-attackÂ playÂ yielded divided in the 16thÂ minute.
Ghana earned a corner-kick and in-form Udinese midfielder Agyeman-Badu glided in a cross which was headed in by captain Mensah.
The Black Stars could have doubled the lead in the 23rdÂ minuteÂ but referee Eddy Maillet waived calls for a penalty after Gyan was fouled insideÂ the box.
Sudan took charge of possession and pinged the ball around as Ghana sat back to defend the two-goal lead.
But Mohammed Abdallah were nearly punished twoÂ minutesÂ after the interval as Ghana went on the counter but Gyan who scurried with the ball intoÂ the boxÂ shot feebly to hit the stretched leg of the Sudan goalkeeper.
In the 47thÂ minute, right-winger Inkoom was put through by Pantsil and the FC Dnipro man passed to Muntari who missed his timing.
The ball dropped to Kwadwo Asamoah still insideÂ the boxÂ but his carpet shot agonizingly missed the goal by inches.
Ghana coach was forced to shuffle his cards on 56Â minutesÂ after centre-back Isaac Vorsah was red carded for punching a Sudanese in an off-the-ball incident.
The North Africans failed to takeÂ advantageÂ of their numerical strength as the Serb tightened his back line by replacing Muntari with Lee Addy.
Goalkeeper Kwarasey pulled a superb and he parried a powerfulÂ drive forÂ a corner-kick which was eventually wasted byÂ the homeÂ team
Both teams went into the final qualifier tied on 13Â pointsÂ but Ghana were on top of the Group with superior goal difference.
However, Sudan could qualify to Gabon and Equatorial Guinea as one of the best second-place teams.
Ghana, four-time African champions, finished second at the last Nations Cup inAngola.