The Tunisian outfit made it to the semi-finals of the competition last season having dropped down from the CAF Champions League, losing out to compatriots and eventual winners Sfaxien in the last four.
And, as they kicked off their bid to go a step further this time around, Edem Rjaibi scored the only goal of the match in Angola to give Bizertin control of the tie.
2012 runners-up Djoliba, meanwhile, made a losing start to their campaign, going down 2-1 at Don Bosco of the Democratic Republic of Congo.
Hamidou Sinayoko gave the visitors an early lead, before Wa Kubanza Ushindi and Eric Kabulo fired the hosts to a shock victory.
Djoliba will be keen to turn in a better performance on Sunday or face making a premature exit.
Cara Brazzaville were another side to pull off a first-leg upset and they will be looking to defend their 1-0 lead away from home against 2006 champions Etoile Sahel on Friday.
The Tunisian club had not lost in 11 competitive fixtures prior to their defeat in the opening leg.
SuperSport United of South Africa will feel confident of progressing to the next round, taking a 2-0 lead to AFC Leopards on Saturday, while St Michel United of the Seychelles face an uphill struggle to qualify, trailing 5-1 against Zimbabwe's How Mine.
Bayelsa United shook of the cobwebs of having not played competitively since October to pick up a goalless draw at Kondzo, while fellow Nigerian side Warri Wolves were similarly untroubled by their long lay-off as they claimed a 3-2 victory against Union Douala. Both sides return to home soil for the second leg.
Elsewhere, AS Kigali of Rwanda take a 1-0 lead to Sudan's Al Ahly Shendi, Gamtel aim to overturn a two-goal deficit at Difaa El Jadida, Medeama try to press home their 3-0 advantage over Maghreb Fes, and the ties between Ferroviario Beira and ZESCO United, and FC MK and Ismaily await their first goals.
ASEC Mimosas and Ebusua Dwarfs both have 2-0 leads to safeguard against CO Bamako and Petro de Luanda respectively, Red Lions are a goal down to CS Constantine ahead of the second leg, while Douanes and Wadi Degla have a goal apiece.
