The dangerous Linda Eshun equalised for the visitors with 13 minutes to time with a cleverly worked out free kick which involved Portia Boalcey.
Boalcey also hit the woodwork with the final kick of the game as Kenya survived at the death.
Buoyed by free entrance granted by Football Kenya Federation, an estimated 5,000 crowd, including Ambassador Yvonne Khamati, FKF vice president Doris Petra and Harambee Stars coach Sebastian Migne, thronged the 60,000-seater facility to watch the match.
"It was good we scored first. We allowed them more into the game and conceded from the set piece. I will try and fix those areas in the remaining games before we head to the championship," Ouma said.
And the supporters were thoroughly entertained in this clash, which serves as a build up for both teams ahead of the continental showpiece.
"We will try and lobby to help these girls, they have so much talent and firepower and they atleast deserve to play in Ghana," said Khamati.
Kenya, who qualified after Equatorial Guinea were disqualified for fielding an ineligible player following an appeal by Football Kenya Federation, is pooled in a tough Group B alongside South Africa, Nigeria and Zambia.
Ghana will face Mali, Algeria and Cameroon in Group A.