Jordan, who is on loan at Crystal Palace from Swansea City, opened the scoring for his country in the fourth minute of the match.
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Jordan Ayew scores brace as Ghana win Afcon 2019 qualifier in Ethiopia
It was the perfect return to the Black Stars squad for Jordan, who along with his brother Andre, last played for Ghana in a World Cup qualifying draw with Congo Brazzaville in October 2017.
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He added a second from the penalty spot midway through the first half.
The result puts Ghana second in Group F on six points from three matches. They are a point behind leaders Kenya who have played one game more.
Kenya's home match against Sierra Leone this weekend was cancelled because Sierra Leone are still serving a global ban from football.
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It means the qualifying picture for Group F remains unclear.
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