The midfielder broke the deadlock in the 67th minute at the Stade Chedly-Zouiten in Friday's encounter as the hosts crashed out of the competition.
Realistically, Al Ahli Benghazi needed maximum points against the Tunisians and from their final pool match at ES Tunis.
Defeat means Jozef Vukusic's men are four points adrift of ES Setif with just one match remaining.
However, three points for Sfaxien means they can now look forward to the semi-finals as Es Tunis - who have matches to play - are unable to catch their tally of 10 points.
Neither team was able to find the breakthrough in a tense first half.
But Sassi made the difference shortly after the hour mark, bagging the only goal of the game, much to the delight of head coach Hamadi Daw and his side.
'You couldn’t blame Trent Alexander-Arnold if he wanted to play for Real Madrid – I hope he stays, but even with Mo Salah, I would understand if he decided to leave': Former Liverpool defender explains why he’s braced for key Anfield exits
‘Sven asked if I’d like to play for England – even to be considered made me proud, but I don’t think they really wanted a foreign player in the national team’: Former Premier League star reveals conversations over converting nationality
