Second half substitute Hamza Younes notched Sfaxien's goal in the 77th minute after a great solo work in the box, a goal which was enough to hand the Tunisian's first spot in the African Champions League quarter final group A with six points.
The home defeat leaves Kabylie bottom of the group with three points with both Asante Kotoko of Ghana and Egyptian Ahli in second and third spot respectively with four points each.
The next round of the African Champions League quarter final will see Sfaxien take on Kabylie in Tunisia, while Ahli and Kotoko will go head to head in Cairo in two weeks time.
In group B, Ivorian side Asec Abidjan beat two times champions Enyimba of Nigeria 3-0 in the Ivorian capital, while South African champions Orlando Pirates were held at home to a 0-0 draw by Ghanaian club Hearts of Oak.
The win leaves Asec on top of group B with six points followed by Enyimba with four in second and Pirates with three points in third, while Hearts' draw earned them their first point of the quarter finals.