The West Ham United winger Ayew kept his nerves to score what proved to be the game's only goal from the spot after 32 minutes.
Uganda who are returning to the continent's flagship tournament after a 39-year absence started the game on a high note, and Tony Maweje saw his long range effort causing no problems to Ghana's goalkeeper Razak Brimah.
But Ghana took the upper hand from now on, with winger Christian Atsu being the master of his side's speedy attacks. Atsu provided Andre Ayew, his brother Jordan and captain Asamoah Gyan with numerous crosses that missed the target every time. The West Africans best chance fell to the Ayew brothers, when Jordan beat his marker to find Andre, but the latter's shot was stopped by Denis Onyango in thee Uganda post.
After 31 minutes, Atsu passed to Gyan who was fouled inside the vital area by Isaac Insinde, and from the spot Andre Ayew made no mistake.
The second half was a different story as Uganda waved off their first half shaky performance to threat Ghana's defense more than once. Maweje, Farouk Miya and captain Geofrey Masa all tried their luck but missed the clinical touch.
And the last word was to be Atsu's once again, as the winger weaved past his marker to strike, but for Onyango to make the save five minutes from time.
Total Man of the Match.
Christian Atsu (Ghana)
Milutin 'Micho' Sredojevic (Head Coach, Uganda)
We haven't been here for 39 years. In the first half, we had what I call stage fright. We comitted a mistake that I cannot explain and Ayew scored. At halftime, we needed to awaken the players so that they believe we can play in tournaments like this. We made a risk at the latter stages playing 3-2-5 but it didn't work. I am very proud of my team and will not look for individual mistakes. My team has shown that we have the technical and physical ability but we still have to work more. We will play against giants Egypt and Mali and we will make sure to give 200% of our efforts.
We came with a mission to prove that we didn't qualify by accident, and I beleive we showed that. We showed that we can play even for more than 90 minutes. But sometimes there are some naive mistakes maybe because of the pressure of being a goal down. I have learnt that at this level of competition we cannot make silly mistakes like what we've done and we will not do that against Egypt and Mali.
We have done everything to get a good result and this have been a great lesson for us. We showed we are capable to play against the best. I congratulate Ghana who are always a top team. We will have two key players back from suspension and I believe we can do better against Egypt.
Avram Grant (Head Coach, Ghana)
I'm happy with the three points. We could have played better but winning is the most important in tournaments like this. We had to take on the pressure in the second half but at the end of the day I am happy.
Uganda is a very tough team and playing against them is never easy. We got a few chances but we won. The second game will be different but there are no easy games in this tournament.
We shall wait and see Baba Rahman's injury. It is only the first game and the most important is to win. Andre and Jordan Ayew had a good team. In the second half we were a bit fatigued and the players wanted to keep the threee oints, and we played in a clever way to win the game.