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.
It was a memorable win for the Liberians against Kabylie who are among the 10 most successful clubs in African competitions.
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 another blow to Algerian football, after the Desert Foxes were eliminated from the recent Africa Cup of Nations at the group phase.
Kabylie's loss was followed by defeat for another Algerian side, Mouloudia Alger, who are also former African champions.
They were beaten 2-1 away to debutants Bechem United of Ghana, but will at least have an away goal to take into their return leg next weekend.
Elsewhere, Rayon Sports of Rwanda are virtually assured of a last-32 place in Africa's second-tier club competition after beating 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 on security grounds.
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.
Record three-time title-holders CS Sfaxien of Tunisia are among 12 clubs who received byes into the round of 32.
Like the Champions League, the Confederation Cup will have a new look this season and increased prize money.
The number of qualifying rounds before play-offs against Champions League last-32 losers has been cut to two and the group phase expanded from eight clubs to 16.
Prize money has been given a 170% boost, including $1.25m (£1.16m) for the winners and $275,000 (£220,000) for the lowest-placed group finishers.
Monrovia Breweries of Liberia made a dream African Confederation Cup debut by trouncing twice former African champions JS Kabylie of Algeria 3-0 in the first leg of their preliminary tie.