The Tunisian club, who have featured in the last three African Champions League finals, lead the group on goal difference from Cameroon outfit Coton Sport, who were 2-1 victors over Angola's Recreativo Libolo.
After a scoreless first half, Esperance had the lead on 48 minutes through Oussama Darragi but then relied on the outstanding saves of Ben Cherifia to secure victory.
Good fortune also favoured Esperance when Sewe's Ocansey Mandela crashed the ball against the visitors' crossbar much to the dismay of a heaving capacity crowd.
Coton Sport were worthy winners over Recreativo thanks to goals in either half from Alexis Yougouda, the top scorer in the tournament with six, and Emmanuel Mbongo.
Libolo pulled one back in the closing stages through Ruben Gouveia but it was just a consolation.
At the half way point both Esperance and Coton Sport have six points from three matches, while Recreatico Lubolo and Sewe Sports have three.
The top two sides from each group advance to the semi-finals.
Fixtures will now be reversed for the next round of matches with Esperance hosting Sewe Sports on August 31 and Coton Sport travelling to Libolo the following day.
(Reporting by Nick Said; editing by Mark Pangallo)
