The team from southeastern city Aba were paired with Horoya of Guinea in the quarter-finals, and the winners of the two-leg tie will probably face Pyramids of Egypt in the semi-finals.
Horoya and Pyramids were the most impressive sides in the six-matchday group phase, finishing six and five points respectively ahead of the runners-up in their sections.
Enyimba are the most successful Nigerian club in African competitions with four titles — two each in the CAF Champions League and CAF Super Cup — but the last success came in 2005.
The Nigerian outfit failed to click in Group D until the final round last weekend when they travelled to the Ivory Coast and trounced San Pedro 5-2 with Victor Mbaoma scoring twice.
The victory margin was surprising as Enyimba had battled in previous away matches and scored just six goals in five other group games.
Dolphins came closest to bringing the Confederation Cup — the African equivalent of the UEFA Europa League — to Nigeria by finishing runners-up to FAR Rabat of Morocco 15 years ago.
Holding Renaissance Berkane to a 1-1 draw in Morocco last Sunday will encourage Zanaco of Zambia, but it difficult to imagine the Lusaka bank club eliminating star-stacked Pyramids.
In the other quarter-finals, Al Masry of Egypt face Berkane and Al Nasr of Libya meet Hassania Agadir with the two Moroccan clubs favoured to advance.
Agadir were eliminated at the last-eight stage last season while Berkane got to the final, where they lost on penalties to Zamalek of Egypt.
Draws
Quarter-finals
Zanaco (ZAM) v Pyramids (EGY)
Al Nasr (LBA) v Hassania Agadir (MAR)
Al Masry (EGY) v Renaissance Berkane (MAR)
Enyimba (NGR) v Horoya (GUI)
First legs: Mar 1, second: Mar 8
Semi-finals
Zanaco/Pyramids v Enyimba/Horoya
Masry/Berkane v Nasr/Agadir
First legs: May 3, second: May 10
Note: final will be played on May 24 at a neutral venue to be announced
