Celtic, who managed to hold Mamelodi Sundowns to an impressive goalless draw in the DStv Premiership in midweek, were without influential captain Ndumiso Mabena and Victor Letsoalo.
The host hit the breakthrough early on through Godwin Aguda, who managed to find a way past goalkeeper Sipho Chaine.
John Maduka's pushed for an equaliser in the latter stages of the first half, but the Nigerian side proved difficult to overcome on virtually all fronts.
This then saw the home side go into the halftime break two goals to the good as Aguda completed his brace.
Siwelele Sa Masele battled and battled early in the second half, but fell further behind after Fortune Omoniwari give the Pride of Rivers a third.
The Pride of Rivers took charge on all fronts to see out the win and with that confirm progression to the next phase.