They are the first of five countries to qualify from the African preliminaries and achieved it with two matches still to play.
Sulley Muntari, who Inter Milan coach Jose Mourinho said may be suffering with his energy levels because he is fasting for Ramadan, put Ghana ahead in the 14th minute.
Chelsea's Michael Essien added a second 10 minutes into the second half, scoring from 20 yards out after picking up a loose ball.
Ghana's win, combined with a 1-1 draw for closest rivals Mali in Benin, ensured the Black Stars went seven points clear at the head of Group D.
Mali, who had led from the 72nd minute when their new striker Mamadou Samassa netted on his debut, conceded a goal three minutes from time in Cotonou. Samassa recently switched his footballing nationality from France.
Another former French junior international Nabil Taider scored for Tunisia as they drew 2-2 in Nigeria to maintain a two-point lead in Group B.
Oussama Darragi scored an equaliser from a tight angle in stoppage time of a storming match in Abuja, dealing a large blow to Nigeria's qualification aspirations.
Nigeria had taken the lead in the 27th minute after a superb finish from Peter Odemwingie but Taider's reply came within two minutes.
Nigeria then survived some anxious moments before restoring their lead when a cross from Taye Taiwo set up a tap-in from close range for substitute Michael Eneramo in the 81st minute.
Darragi's equaliser set off a storm of protest from home fans who pelted both teams with objects after the goal and at the final whistle.
Morocco's Adil Taarabt came on as a substitute and dribbled through the Togo defence in stoppage time in Lome on Sunday to give his country a 1-1 draw in their Group A match.
Togo had scored after four minutes through Moustapha Salifou and the draw against the group's bottom side is a blow to their hopes of qualifying. Togo (five points from four matches) are second behind Gabon (six points from three matches).
Only the five group winners qualify for the World Cup from the final phase of African qualifiers. Africa will have six representatives in 2010 because hosts South Africa are automatically in the field.
