The Ghanaians managed to stay afloat after a spirited second half display from the Cranes.
Ghana coach Avram Grant heaved a sigh of relief with several questions marks about the ability of his team to go all the way.
Andre Ayew opened the scoring from the spot kick in the 30th minutes after Asamoah Gyan was tucked by Isaac Insinde.
The West Ham United made no mistakes as he converted to give the Ghanaians the lead in Port-Gentil.
It was Andre's 7th goal at the Africa Cup of Nations to equal Asamoah Gyan and Osei Kofi as Ghana's all time leading scorer at the continental showpiece.
The Black Stars could have scored more with Christian Atsu, Andre Ayew and Asamoah Gyan coming close in the first half.
But it was the Cranes who asked several questions in the earl exchanges with Ghana right-back Harrison Afful struggling to contain the pace and trickery of Joseph Ochaya.
The East Africans looked more positive on the left flak with Tony Mawejje making things uncomfortable for the Black Stars.
Ghana began to find their rhythm by building up slowly from the back with John Boye and Daniel Amartey as the Cranes created a huge wall at the heart of the park.
Amartey's tendency to go upfront created void in the midfield which allowed the Cranes easy access to the ball.
Gyan came close in the 15th minute as he heads wide inches off the target after a sweet cross from Harrison Afful with Amartey not covering quickly.
Atsu moved away from his marker into the box but his cross was intercepted for a corner - great opportunity to open the scoring on the 17th minute mark.
Again the Newcastle United wideman created space to fire from close range but effort skyrockets.
Perhaps the biggest chance fell to Andre Ayew who missed with a miscued shot before he made amends from the spot kick.
Coach Avram Grant was forced to replace Abdul Baba Rahman as the Schalke defender's ankle kicked as he attempted to stretch for the ball, falling to the ground in one move-turned and signaled to the bench to be substituted.
Versatile Anderlecht man Frank Acheampong replaced him slotted in nicely, provided cover from the left-back for 'shaky' goalkeeper Razak Brimah.
Uganda had the perfect chance to pull parity but Isaac Insinde touch from a great cross was too feeble to worry Ghana.
The second half belong to the Cranes who brought several legs forward in search of the equalizer, forcing Amartey and Boye to make many clearances.
But the Ghanaians defence held their verve to grind out an important first win against their recent nemesis.
Grant substitution did little to enhance his image after he was booed for replacing Asamoah Gyan with Emmanuel Agyemang-Badu.
Aston Villa striker Jordan Ayew will come under a lot of flak for his perceived poor performance against the Cranes.
The Black Stars will next battle Mali in their second group game.
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