Kabylie, whose last African success came 15 years ago, fired Tunisian coach Sofiene Hidoussi after the Monrovia mauling and hired Algerian Mourad Rahmouni.
Boulaouidet levelled the preliminary tie on aggregate by scoring from close range on 62 minutes. Billel Mebarki beat the Liberian goalkeeper from long range 11 minutes later to complete the scoring, and another great Kabylie fightback in the competition.
The Algerian "Canaries" eliminated Gabonese club Missile on penalties six years ago after trailing by three goals from the first leg.
Kabylie completed a successful weekend for Algeria in the secondary African club competition after Mouloudia Alger eliminated Bechem United of Ghana Saturday.
Both Nigerian clubs were eliminated with Ifeanyiubah losing a penalty shootout against Al Masry of Egypt in Ismailia having suffered a 1-0 second-leg defeat.
Ahmed Shokry converted a first-half penalty to cancel the 1-0 lead African debutants Ifeanyiubah established last weekend.
Wikki Tourists edged visiting Sierra Leone armed forces outfit RSLAF 1-0 in Bauchi thanks to a Mustapha Ibrahim penalty 14 minutes from time.
But the winning margin was insufficient for the Nigerians as they trailed by two goals from the first leg.
Former New Zealand international Jeremy Brockie opened the scoring for SuperSport United in a tense 2-1 victory over Saint-Michel Elgeco Plus of Madagascar in Pretoria.
That was also the overall score following a goalless draw on the Indian Ocean island.
Rayon Sports of Rwanda, Etoile of Congo Brazzaville and Ittihad Tanger of Morocco were the other clubs to book last-32 places Sunday.
The round of 32 will be played during March.