Jackson Muleka scored 19 minutes into the match to separate the two sides.
The second leg in Ndola next week will see Tesco needing to score at least a goal to push the match to a penalty shootout while avoiding conceding against a TP Mazembe side which knows that an away goal could further their advantage.
Yassine Chammakhi converted from the penalty spot while Bilel Khefifi and Oussama Darragi also weighed in with goals each for Club Africain’s win.
Mohamed Musa grabbed Al Hilal’s consolation goal which they hope could count for an away goal advantage when they host the Tunisians.
Meanwhile, Baher El Mohamady and Karim Bambo were on target as Egyptian side Ismaily beat Cameroonian giants Cotonsport 2-0 at home.
Returning to the Champions League after an eight-year absence, Ismaily continued their march to the group phase with the home win after also an impressive outing in the preliminary round.
Cotonsport searched for an away goal, but Ismaily were steely in their defending.
In Kinshasa, AS Vita recorded a heavy 4-1 win over Bantu FC of Lesotho.
Vita’s hero in the Caf Confederation Cup last season Jean-Marc Makusu translated his form into the Champions League with a brace, while Francis Kazadi and Chadrack Lukombe Muzungu added their names onto the scoresheet.
Johannes Molapo hit Bantu’s consolation as they now need to score three goals without reply at home to reach the group stages.
In Owando, Congo Brazzaville, Zimbabwean champions FC Platinum salvaged a 1-1 draw with AS Otoho.
William Stima struck FC Platinum’s equalizer after Matheus Botamba had thrust Otoho ahead.
The away goal by the Platinum Miners could be their gateway to a maiden group phase appearance when they host the Congolese side next week.
But they could be wary of Otoho, who eliminated last season’s semi-finalists Primeiro Agosto in a contest that included a spirited away performance.
Elsewhere in the Caf Confederation Cup, defending champions Raja Casablanca began their title defence on a high with a 5-0 thrashing of Gabonese side Cercle Mberi.
The 2018 Confederation Cup top-scorer and Raja forward Mahmoud Benhalib picked up from where he left from last season, contributing a goal in the rout.
Badr Banoun and Mohamed Shaban were also on target while Adberrahim Achchkir scored from the penalty spot as a Cercle Mberi defender also scored an own goal.