Tunis, champions in 1994 and 2011, will hold hopes of winning the tournament again, particularly after favourites Al Ahly were dumped out of the competition in March.
However, Tunis' Group B opener proved to be more troublesome than anticipated as their Algerian visitors stole a commendable victory.
The result could have been even worse were it not for a string of important saves by Moez Ben Cherifia, with the away side producing a determined display at Stade Olympique de Rades.
Setif's rapid forwards proved a constant headache for the home defence and the underdogs twice capitalised on mix-ups at the back.
Rachid Nadji broke the deadlock in the 24th minute and, although things remained as they were until the break, Setif wasted no time in increasing Tunis' misery after half-time.
El Hedi Belameiri struck just three minutes into the second half to double the lead, with Idriss Mhirsi's reply for Ruud Krol's side five minutes later proving in vain.
Prior to Saturday's game, Al Ahly had been the only team to inflict a home Champions League defeat on Tunis since 2005, winning 2-1 in November 2012.
Tunis' next Champions League fixture sees them face a tough trip to Al Ahli Benghazi on May 24, while Setif host another Tunisian side - CS Sfaxien - a day later.
