Wits needed to overturn a 1-1 draw from the first-leg at home two weeks ago, but were in for a torrid time, despite a positive start.
An attempted volley by Daine Klate after 22 minutes following a flick on by Eleazar Rodgers went over the top.
Enyimba were certainly under immense pressure early on as they had to clear off the line following a great scissor kick by Klate six minutes later.
The People's Elephants almost went ahead with virtually their first attack of the game, but Chinonso Okonkwo failed to find the target.
Former Orlando Pirates goalkeeper Fatau Dauda was called upon five minutes to half-time when Keagan Ritchie tested him with a long-range shot which he was able to punch safely to touch.
Minutes following the restart, Ike Ibenegbu fashioned a half-volley from close-range just wide, with Abdulrahman Bashir unable to steer in the follow through effort.
On 55 minutes, the Students pulled in a creeping header at the far post from Bongani Khumalo but Dauda was quick to stop the effort.
On 65 minutes, Bashir dropped deep and played the ball to Freedom Omofoman, who dragged his last man before firing wide from a good scoring position.
Enyimba were handed a further boost following the dismissal of Edwin Gyimah for a rough challenge on Austin Oladapo in the 68th minute.
With four minutes to go, Wits had a golden chance to clinch their progression with a two-on-one scenario, but Rodgers couldn’t get his head on the delivery from Thobani Mncwango.
The Clever Boys were handed a scare in added time in the form of a penalty after Omofoman was upended following his run through the box.
However, the penalty was saved by Kyle Peters following Oladapo’s attempt and Ifeanyi Anaemena only struck the side-netting from the rebound.
In the end, though, it was of little trouble to the Nigerian outfit as they held on for a group stage berth, edging the tie on the away goals rule.
Enyimba: Dauda, Abalogu, Udo, Oladuntoye, Mohammed, Anaemena, Ibenegbu, Chukwude, Oladapo, Okonkwo (Omofoman 57'), Bashir.
Subs: Afelokhai, Governor, John, Alalade, Leonard, Udeagha, Omofoman.
Wits: Josephs (Peters 46'), Mkhwanazi, Khumalo, Klate, Ritchie, Claasen (Monare 46'), Mncwango, Frosler. Myeni, Gyimah, Rodgers.