Care-taker coach Maxwell Konadu lost his first major game in charge of the former world champions in a crucial away game in Nakivubo
The Hippos will be in Ghana in a fortnight for the second leg and the 2009 World Cup winners have to put in a great deal of effort to overturn the results in order to reach the final round of qualifying.
The team which comes out top is scheduled to meet either Morocco or Gambia.
Maxwell Konadu's side drew first blood after just five minutes when Michael Anaba scored in Nakivubo.
But the home side drew level three minutes later through striker Julius Ogwang before Joseph Mpande gave the Hippos a 2-1 lead.
Just before half-time, Ogwang scored his second of the afternoon to seal victory for Uganda.
Ghana's attempts to pull a goal back and possibly look for the equaliser in the second half failed to materialise.