Bright Vuni scored the goal for the military side before Bobosi Byaruhanga scored from a direct corner to ensure the tie ended in a 1-1 draw.
In the first leg encounter, the Venoms had picked a 3-1 win at Bombo Military Barracks.
Vuni scored against Vipers in the 10th minute and Byaruhanga would have equalised for the hosts three minutes later.
But his effort went over the bar from close range.
Bernard Muwanga could have doubled the lead for UPDF in the 15th minute but his header, from a nicely delivered corner kick, went wide.
Byaruhanga leveled matters for Vipers in the 23rd minute from a direct corner.
Halid Lwakliwa could have scored the second for the Venoms but his fierce shot was saved by UPDF’s goalkeeper Eric Kibowa.
Ceasar Manzoki failed to find the back of the net in the 33rd minute.
He found himself in a good position but he blasted wide.
The Venoms launched a clinical counter-attack in the 60th minute but a final shot by Jamil Kalisa went out.
Fred Kajoba made two changes in the 65th minute.
Paul Mucureezi and Najib Yiga came on for Allan Kayiwa and Kalisa.
Lawrence Tezikya, Ibrahim Orit and Disan Galiwango came on for Manzoki, Karisa and Aziz Kayondo in the 72nd minute.
A combination between Orit and Tezikya almost produced a second goal for Vipers.
But the latter headed straight into Kibowa’s hands.
The 1-1 draw means Vipers have qualified for the next round courtesy of a 4-2 aggregate.