Andre Ayew struck from 12 yards to give Ghana a winning start to their AFCON campaign in Gabon.
The West Ham forward made no mistake from the spot in the 32nd minute after Asamoah Gyan was brought down in the penalty area.
In a nervy second half the Black Stars were unable to add to their lead but held on to claim a vital three points over Uganda.
The result also means Ghana have now won four of their 11 matches against Uganda.
Avram Grant, a former Chelsea manager, is looking to lead Ghana to a second successive final but go better than 2015 when his team lost to Ivory Coast.
Uganda have also finished runners-up in the continental championship but the trip to the final in 1978 was also the last time they qualified until making the Gabon event.
Ghana also threatened through two Gyan headers, while Ayew and Christian Atsu tested Uganda goalkeeper Denis Onyango.
Uganda came close when Faruku Miya hit the outside of a post but they could not force their way back into the game.
It was a disappointing return for Uganda, who are playing at their first Nations Cup since 1978 when they lost in the final to then-hosts Ghana.
The Cranes created few opportunities of note and struggled against the Black Stars, who were happy to defend their lead.
Ghana were far more positive in the first half, with Andre Ayew, his brother Jordan and Atsu posing a huge problem for the Uganda defence.
Andre Ayew should have scored from a great cut-back by Jordan, while Atsu relentlessly tormented defender Isaac Isinde, whose conceded a penalty by tugging back Gyan after losing control of the ball.
The spot-kick gave Andew Ayew his seventh Nations Cup finals goal – one more than the number scored by his father and legendary former Ghana captain, Abedi Pele. But he remains one African title behind his father, who lifted the trophy in 1982.
Ghana had a good chance to add a second late on when Atsu was clean through but his 12-yard drive was superbly saved by Onyango.
The only downside for Grant’s side was an injury to defender Baba Rahman, who was taken off with what looked like a hamstring injury after 39 minutes.
Ghana will next take on Mali on Saturday while Uganda will face record seven-time champions Egypt on the same day.
