Energetic youngster Mohammed Kudus put Ghana ahead in the early minutes of the games.
However the Warriors of Zimbabwe pulled one back through a penalty kick after Alexander Djiku brought down his marker.
Thanks to the tactics of coach Milovan Rajevac Ghana scored again courtesy a strike from Arsenal midfield dynamo Thomas Partey.
In-form captain, Andre Ayew sealed the victory with three minutes to end normal time as he headed into the net from close range.
Ghana will hope for a similar performance or better on Tuesday when they face Zimbabwe in Harare.
Watch highlights below