FUS fought back at home to defeat Club Africain of Tunisia 2-1 with the winner from Ayoub Skouma coming four minutes into stoppage time.
Woeful defending allowed Rivers to level on 33 minutes as unmarked Bolaji Sakin volleyed a cross into the net from close range.
Rotimi went off injured before half-time and Abiodun Akande came off the bench for Rivers, who hope to become the first Nigerian winners of the African equivalent of the Europa League.
Akande had no chance of preventing the 71st-minute winner as a free-kick eluded several defenders and fell to unmarked Nsibambi, who slammed the ball into the far corner.
Ibrahim Chenihi, scorer of four goals in a qualifier, ended a four-match drought by putting former runners-up Club African ahead on 19 minutes in Rabat.
Mohamed Fouzair equalised eight minutes into the second half by converting a penalty awarded for hand-ball.
FUS, beaten by a stoppage-time goal from Mouloudia Bejaia of Algeria in the 2016 semi-finals, scored the winner four minutes into additional time.
A Club Africain defender deflected a free-kick across the goalmouth to unchallenged Skouma, who fired past goalkeeper Farouk Ben Mustapha to trigger wild touchline celebrations.
The results in Kampala and Rabat maintained a cycle of home victories in the group and put FUS and KCCA on top with six points followed by Club Africain and Rivers with three.
Horoya of Guinea won 1-0 away to Mounana of Gabon and lead Group D by one point from SuperSport United of South Africa and title-holders TP Mazembe of the Democratic Republic of Congo.
The Conakry club gained their first victory after two draws thanks to a second-half goal from Seydou Karamba Camara against the pointless Gabonese in Libreville.
Mazembe, the second most successful club in CAF competitions with 10 titles, host SuperSport on Sunday in southern Congolese city Lubumbashi.