An own-goal by defender Nicholas Opoku helped the home side to the victory at the Kasarani Stadium.
Both sides came to close to scoring before the half hour mark.
And it was the hosts who first tested Richard Ofori and the Maritzburg United No.1 pulled a stop to Ochieng Ovella powerful strike from the right.
The Black Stars managed to unlock the Kenya defence with a laser pass, which found Waris at the edge of the box.
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The on-loan Nantes forward had his shirt pulled but managed to slip a pass to Partey whose feeble shot was collected easily by Patrick Matasi.
In the 27th minute, Astu peeled to the left flank inside the area of Kenya and his intended cross to Waris was miscued and feeble.
The Black Stars were seeking their second straight win after an emphatic 5-0 victory over Ethiopia in the opening game, but Kenya with a masterful defensive display were able to deny Kwesi Appiah's charges.
Kenya's breakthrough came in the 39th minute after a period of consistent Ghana dominance. Eric Johana delivered a fine cross into the Ghana box and, under pressure from Michael Olunga, Opoku diverted the cross into his own net.
Watch the goal above...