Having lost their first two Group B matches, ES Tunis were made to work for their 2-1 win against the side they edged for the Tunisian top-flight title last month.
Maher Hannachi gave CS Sfaxien the lead after 47 minutes, converting Ali Maaloul's assist.
But the Tunisian champions produced an inspired response, initially drawing level in the 65th minute through Oussama Darragi.
And Idriss Mhirsi bagged the winner just one minute later to complete ES Tunis' comeback.
ES Tunis still sit bottom of Group B, but are just two points behind leaders ES Setif.
Sunday's other match saw Congo's TP Mazembe move to the top of Group A with a 1-0 success against Zamalek of Egypt.
Rainford Kalaba scored the game's only goal in the 13th minute.
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