Tagoe struck after just five minutes, his Partizan Belgrade team mate and strike partner Adiyiah scored on 30 minutes and Muntari came off the bench in the second half to seal a convincing victory for Africa's top-ranked team.
It was a second win in three qualifying games for Ghana.
Also on Sunday, Niger enhanced their chances to qualify for the finals after defeating Sierra Leone 3-1 at home.
The hosts are Second of the group G with six points, just one behind leaders South Africa.
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