All the goals came during the second half at a packed Monrovia stadium with state president Ellen Johnson Sirleaf among those who saw Mitis Mulbah score twice and Benjamin Sarkoh once.
Mulbah broke the deadlock in a goalmouth scramble on 58 minutes and completed the rout after Sarkoh punished a blunder from Algeria goalkeeper Malek Asselah.
The unexpectedly heavy loss for Kabylie was the latest blow to the image of Algerian football.
After a disastrous start to the group phase of the 2018 World Cup qualifiers, the national team were shock first round casualties at the Cup of Nations in Gabon last month.
Rayon Sports of Rwanda are virtually assured of a last-32 place in the second-tier African club competition after walloping newcomers Al Salam Wau of South Sudan 4-0 in Juba.
Savio Nshuti triggered a second-half goal rush by netting after 54 minutes and Pierrot Kwizera, Nova Bayama and Moussa Camara scored in the final quarter as Salam collapsed.
Bosnian Enes Sipovic notched the second-half winner as Ittihad Tanger of Morocco, experiencing continental football for the first time, came from behind to defeat Douanes of Niger 2-1 in Niamey.
There was more success for Morocco as second division outfit MAS Fes used home advantage to build a 3-0 lead over former African champions CARA of Congo Brazzaville.
An embarrassing blunder by the Congolese goalkeeper, who allowed a harmless low cross to slip from his grasp, gifted Ivorian Koffi Boua the first goal for 2011 Confederation Cup winners Fes.
Al Hilal Benghazi of Libya overcame the handicap of not being able to play at home by beating fellow Confederation Cup debutants Ulinzi Stars of Kenya
1-0 in Cairo.
Ahmed Al Abbar scored the winner just after half-time for Hilal, who were forced to move the fixture to Egypt because of post Moamer Kadhafi regime violence in Libya.
Volcan of the Comoros exceeded expectations by drawing 0-0 with Vipers of Uganda in Kampala, raising the prospect of a first overall African success by a club from the multi-island Indian Ocean nation.