Bakr el Helali gave Berkane a 10th-minute lead that lasted just 60 seconds before Phillippe Kinzumbi equalised in northeastern Morocco.
Mazembe were reduced to 10 men midway through the second half when Tandi Mwape was sent off and the late goal rush began when captain Larbi Naji put Renaissance in front a second time. Youssef el Fahli converted an 88th-minute penalty to edge Berkane in front on goal aggregate and he put the outcome beyond doubt with another goal six minutes into added time.
Beaten 1-0 in the first leg last Sunday after conceding an added-time goal, Berkane triumphed 4-2 on aggregate and face Orlando Pirates from South Africa this Friday in the title decider in Uyo, Nigeria.
An hour before the match in Berkane kicked off, Pirates suffered a shock 1-0 home defeat by Al Ahly Tripoli from Libya, but advanced 2-1 on aggregate.