The Port Harcourt outfit host Group A pacesetters FUS Rabat of Morocco Wednesday in a must-win match for the west Africans.
They struck four against Real Bamako of Mali and three against Al Merrikh of Sudan in Champions League qualifiers.
Demoted to the second-tier Confederation Cup, Rivers maintained a perfect home record with a 2-0 play-off victory over Rayon Sport of Rwanda.
Surprise 2010 Confederation Cup winners FUS are likely to be more stubborn defensively than the other three African visitors to Port Harcourt.
But Rivers captain and defender Festus Austine believes his side will not only beat the Moroccans, but go on to lift the trophy.
"Our aim is to become the first Nigerian winners of the Confederation Cup,"
he told reporters. "We are good enough to achieve that goal."
Austine and fellow defender Ifeanyi Nweke watched a 3-1 group-opening loss at Club Africain of Tunisia from a stand this month due to suspensions.
Some of the wounds suffered by Rivers in the match were self-inflicted with Togolese Joseph Douhadji conceding an own-goal and Emeka Ogbugh blazing a penalty over the crossbar.
"Those mistakes are history," stressed Austine. "All we are thinking about is how to defeat FUS and get back into contention for first place."
Kampala Capital City Authority (KCCA), the first Ugandan qualifiers for a CAF club group stage, are another side desperate for three points.
Beaten 3-0 at FUS, KCCA hope for goals from leading scorer Geoffrey Sserenkuma when they host Club Africain.
Like FUS, title-holders TP Mazembe of the Democratic Republic of Congo, CS Sfaxien of Tunisia and Zesco United of Zambia are seeded to win groups.
Record three-time Confederation Cup winners Sfaxien cannot have been happy with a 1-0 Group B win at home to outsiders Mbabane Swallows of Swaziland.
They face what is likely to be a tougher task Tuesday away to Mouloudia Alger of Algeria, who began with a 1-1 draw at Platinum Stars of South Africa.
Boosted by the return from Angola of former star Tresor Mputu, Mazembe tackle Horoya in Guinea having opened with a 2-0 Group D win over Mounana of Gabon.
Now 31, Mputu achieved a remarkable feat in 2007 by finishing leading scorer in the Champions League and Confederation Cup.
Group C favourites Zesco take a multi-national squad including Kenyans David Owino and Jesse Were to Al Hilal Obeid of Sudan.