Defender Ebube Duru was sent off just before half-time after being shown a second yellow card during the Group B clash in Luanda.
The match was moved to the Angolan capital because the home ground of Pembe in Kinshasa is not up to international standards.
A 53rd-minute goal by Ghanaian Paul Acquah took the Port Harcourt outfit to six points, two more than ASEC Mimosas of the Ivory Coast and Diables Noirs of Congo Brazzaville.
Rivers have risen from the bottom to the top of the mini-league within three rounds after suffering a three-goal drubbing away to Diables in matchday 1.
United are hoping to become the first Nigerian winners of the African equivalent of the Europa League and host Pembe on March 8 in the next round.
Marumo Gallants of South Africa surrendered the last perfect group record when losing 2-0 away to USM Alger of Algeria in a top-of-the-table Group A showdown.
Abderrahmane Meziane scored his third goal of the campaign by slamming a loose ball into the corner of the net six minutes before half-time.
Despite territorial dominance, USM had to wait until one minute from time to seal victory as captain Zineddine Belaid nodded past Zimbabwean goalkeeper Washington Arubi after a free kick.
USM have seven points and Marumo six, and Saint-Eloi Lupopo of DR Congo lie third after edging Al Akhdar of Libya 1-0 to collect their first points.
TP Mazembe of DR Congo, winners of 11 CAF titles, surprisingly lost 2-0 at home to leaders US Monastir of Tunisia in Group D with Malian Boubacar Traore and Zied Aloui scoring.
Young Africans of Tanzania are second, one point above Mazembe, after drawing 1-1 away to Real Bamako of Mali, who levelled through Emile Kone in added time.
FAR Rabat of Morocco, one of three former African champions among the 16 title contenders, lead Group C thanks to a 2-0 win over Egyptian visitors Future.
Mentioned in the news story
Confederation Cup
Motema Pembe
Rivers United
