The Buccaneers saw fit to give Tshegofatso Mabasa a start following his impact from the bench against Swallows FC and granted Innocent Maela a start after a while on the sidelines.
A confident start from the Soweto giants followed through a powerful first-time shot from outside the area by Vincent Pule, but goalkeeper John Barinyima got across to beat away three minutes in.
Pule was involved again in the Buccaneers' next threat to goal 12 minutes gone when he drilled a free-kick off the top of the crossbar after a foul on Fortune Makaringe.
It was at this particular point that Enyimba started opening up following the next eight minutes as goalkeeper Wayne Sandilands parried a smart cross-cum shot.
Enyimba started to pull numbers back and provided Sandilands with more work from a spell of two promising attempts from point-blank range.
The Buccaneers still maintained the lively spark from the earlier exchanges, as Pule managed to see a lot of the ball and his runs on and off the ball proved troublesome for the Nigerian outfit.
Pirates suddenly began to find life difficult closer to the last 30 minutes as the Peoples Elephant bombarded the opposing goal but Sandilands was equal to every threat.
With the tempo of play evened and the host still on the ascendancy, the Buccaneers closed shop ten minutes from time with Siphesihle Ndlovu sacrificed for Wayde Jooste.
Enyimba had the ball in the net in additional time through Kadri Timileyin from a long ball, but it disallowed for offside much to the home side's disappointment.
However, the home side were rewarded in the dying seconds when Cyril Olisema finished off a cutback from close-range to join the Buccaneers in the quarter-finals of the Confederation Cup, while ES Setif and Al-Ahli Benghazi miss out.
Pirates: Sandilands, Nyauza, Maela, Mabaso, Mako, Ndlovu, Motshwari, Makaringe, Mntambo, Pule, Mabasa.
Subs: Sesane, Muwowo, Zungu, Sam, Dlamini, Jooste, Monyan