The thrashing completed a miserable trip to north Africa for the Dakar club after officials complained about being given an old bus and staying at a hotel far from the stadium.
Berkane said they were victims of poor treatment when in Senegal last weekend for the first leg, which they lost 2-0 after missing a penalty.
Renaissance qualified 5-3 on aggregate for a second successive appearance in the group phase of the second-tier African club competition.
It was the third time in the 2018/2019 CAF club competitions that Moroccan sides have eliminated Senegalese opponents.
Jaraaf successfully defended their first leg lead for 26 minutes and then conceded twice within three minutes as Burkinabe Alain Traore and Togolese Kodjo Fo-Doh Laba netted.
Hamdi Laachir made it 3-0 on the night and 3-2 on aggregate for Berkane by scoring five minutes before half-time.
Jaraaf pulled one goal back in the opening minute of the second half only for Laba to score his second goal of the match before another Burkinabe, Issoufou Dayo, completed the rout.
Hassania Agadir hammered Jimma Aba Jifar of Ethiopia 4-0 to ensure Morocco will have at least two teams in the 16-club group draw this Monday in Cairo.
Leading 1-0 from the first leg in Addis Ababa, Hassania needed only 18 minutes to open the scoring at home through Yassine Rami and the other three goals came during the second half.
Ittihad Tanger, the third Moroccan club in action, fell 3-1 away to Zamalek of Egypt in Alexandria to bow out by the same score overall after a goalless first encounter.
A tense north African showdown was not decided until five minutes from time when Youssef Ibrahim struck a third goal for nine-time CAF title winners Zamalek.
Ibrahim Hassan had put the Cairo outfit ahead on the stroke of half-time, Nouaman Aarab levelled on 50 minutes only for Omar el Said to volley the hosts back in front soon after.
Trophy-holders Raja Casablanca are expected to increase the Moroccan representation in the draw to three clubs Sunday after drawing 1-1 away to African Stars of Namibia last weekend.
The much anticipated clash of Kaizer Chiefs from South Africa and Zambian side Zesco United in Soweto proved a flop with the visitors winning 2-1 for a 5-2 aggregate triumph.
A howler from Namibian goalkeeper Virgil Vries gifted Anthony Akumu an early goal for Zesco and another Kenyan, Jesse Were, doubled the lead midway through the second half.
Chiefs, who had entered the match confident of overcoming a 3-1 first-leg loss, had to wait until stoppage time before Zimbabwean Khama Billiat claimed a consolation goal.
Academy side Salitas became the first club from Burkina Faso to reach the group stage of a CAF competition thanks to a 3-1 victory over Libyan visitors Al Nasr in Ouagadougou.
Trailing 1-0 from the first leg, Salitas led 2-0 at half-time and an early second-half goal by Ilias Sawadogo stretched the advantage before Emmanuel Azubuike reduced arrears.