All the goals at the Olympic Stadium in Rades on the outskirts of Tunis came from defenders during a weekend when no striker found the net in the premier African club competition.
Chamseddine Dhaouadi put Esperance ahead after only two minutes, Ammar Jemal equalised just before the half-hour and Sameh Derbali snatched the 77th-minute winner.
The narrow win leaves the most intriguing of the last-eight ties delicately balanced ahead of the return match in Mediterranean resort Sousse next Friday.
The other Saturday quarter-final, a dour struggle between Primeiro Agosto of Angola and TP Mazembe of the Democratic Republic of Congo, ended 0-0 in Luanda.
There were also no goals in the first Friday match with Horoya of Guinea held in Conakry by record eight-time African champions Al Ahly of Egypt.
A few hours later, Senegalese midfielder Isla Daoudi Diomande scored early to earn Entente Serif of Algeria a 1-0 home win over title-holders Wydad Casablanca of Morocco.
After those results, Ahly and five-time champions Mazembe will fancy their chances of reaching the semi-finals in a competition with a $2.5 million (2.1 mn euros) first prize.
But the other two ties are balanced on a knife edge with Etoile, thanks to their away goal, and experienced knockout campaigners Wydad marginal favourites.
The African champions qualify for the 2018 FIFA Club World Cup during December in the United Arab Emirates, where Real Madrid will be the star attraction.
There was an electric atmosphere in Rades with a chase between security personnel and a streaker adding to the drama.
Dhaouadi nodded twice champions Esperance ahead off a free-kick before another centre-back, Jemal, maintained his remarkable record of scoring vital CAF goals.
Etoile, the only team to win all five current and past CAF club competitions, looked like they might sneak a draw until full-back Derbali struck.
Meanwhile, there was far less excitement for a near-capacity crowd in a 50,000-seat Angolan stadium as Primeiro and Mazembe got bogged down in a largely midfield battle.
The home side wasted a good chance when Nigerian Akinfenwa Ibukun fired wide from the edge of the box on 19 minutes after a careless clearance by Ivorian goalkeeper Sylvain Gbohouo.
Mika Miche should have put Mazembe ahead later in the opening half when Primeiro got themselves into a tangle, but his close-range shot was bravely blocked by a defender.