The result means they are now three points off Group B leaders FUS Rabat and two points behind the other Moroccan side, second placed Kawkab Marrakech.
Only the group winners and runners-up will qualify for the semi-finals.
After a barren first half in Sousse, Etoile found their stride after the break.
Alaya Brigui scored twice - in the 57th and 68th minutes - before a goal from Ahmed Akaichi sealed maximum points.
The result keeps Etoile in the hunt for a place in the last four, following FUS Rabat's 3-1 win away to fellow Moroccans Kawkab Marrakech on Friday night which put  FUS top of the table.
Until Friday, Kawkab Marrakech had won all five of their Caf home matches this year, and the defeat to their Moroccan rivals relegated them to second in Group B.
Youssef El Gnaoui put FUS Rabat ahead early on from the penalty spot, with Mohamed El Fakih also hitting a first-half penalty to level the score at 1-1.
Second half goals from captain Abdessalam Benjelloun and Mohamed Fouzair put FUS Rabat in firm control as they secured a well earned victory.
On Sunday, there was one Group A match with favourites TP Mazembe  maintaining their unbeaten run with a goalless draw at Mouloudia Bejaia of Algeria.
That means DR Congo giants Mazembe have seven points from three games so far, and seem certain to take one of the places in the last four.
In the other Group A match, Tanzania's Young Africans were held to a 1-1 draw by Ghanaian side Medeama on Saturday - a result which did little for either side's hopes of progressing out of the group.
Scoring had been a problem for both teams, but it took just three minutes for the deadlock to be broken, when Donald Ngoma struck first for the hosts in Dar es Salaam.
Medeama got their equaliser sixteen minutes later through Bernard Ofiri.
The defending champions Etoile du Sahel secured their first victory of the African Confederation Cup group phase with an emphatic 3-0 win over Al Ahli Tripoli of Libya on Saturday night to remain title contenders.