After losing 5-4 to Nigeria in a thrilling encounter in their first match on Sunday, Oscar Mirambo's men needed to beat Uganda to remain in the running for a place in the semi-finals.
Andrew Kawooya opened the scoring for the Cubs after teaming up with Najib Yiga with a delivery that flashed across goal and squeezed in from a tight angle to the back of the net in the 16th minute.
Ivan Asaba doubled Uganda's tally in the 28th minute and Yiga sealed the result with a header 14 minutes from time.
The result sees Mirambo's side fail to qualify for the global event as they remain winless and lay bottom of Group A with zero points from two matches.
With the win, Uganda now occupies second spot in Group A, three points behind leaders Nigeria who overcame Angola 1-0 in the other game played on Wednesday.
Golden Eaglets' win saw them qualify for the World Cup with a game to spare for the record 12th time.