Farouq Miya scored the winner nine minutes from time in Wednesday's friendly to dampen the occasion for Enyeama - who joined Joseph Yobo in securing 100 caps for Nigeria.
Having made a slow start to Wednesday's clash, the Super Eagles gradually got into gear prior to the break with Ogenyi Onazi and Ahmed Musa proving threatening.
Musa felt he should have had a penalty shortly before the interval when he was brought down by Dennis Onyango.
Referee William Agbovi waved away appeals and did so again in the second half when Cologne forward Anthony Ujah tumbled under a challenge from Shafiq Bakaki.
As Uganda looked to finish with a flourish, Geofrey Massa's trickery gave Nigeria a warning, only for Nelson Ogbonanya to miss the target.
Miya then popped up with the decisive goal after patient build-up play, Enyeama unable to prevent his team falling behind despite getting a hand to the shot.
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