That result left the teams level at 1-1 on aggregate in the secondary African club competition and Ulinzi won 5-4 on penalties to progress.
Vipers, another club competing in the Confederation Cup for the first time, draw 1-1 with Volcan of the Comoros in Moroni to advance on away goals.
After a goalless first leg in Kampala last weekend, Volcan took an early lead at home through Kamal Djabir.
But Deus Bukenya equalised on the half-hour mark with a goal that ultimately proved crucial.
Vipers next opponents will be Platinum Stars of South Africa, who snatched a late 1-0 win over Uniao Songo of Mozambique in Maputo through Ndumiso Mabena.
Platinum qualified 2-0 on aggregate having also won the first leg by a solitary goal.
APEJAS Mfou and Young Sports Academy of Cameroon, 2011 Confederation Cup winners MAS Fes of Morocco and former African champions Mouloudia Alger of Algeria also advanced.
So did Al Hilal Al Obeid of Sudan, Le Messager Ngozi of Burundi, Mbabane Swallows of Swaziland, Ngezi Platinum of Zimbabwe, SC Gagnoa of the Ivory Coast and Renaissance of the Democratic Republic of Congo.