Jonathan Bolingi, one of four Congolese in the Mazembe starting line-up, converted a late first-half penalty to give the visitors a 1-0 half-time lead at Stade Mustapha Tchaker in Blida.
The second leg is next Sunday in Congolese mining city Lubumbashi and a goalless draw will give Mazembe the trophy for the first time after finishing runners-up three seasons ago.
Although Mazembe have won nine CAF titles -- including five Champions League successes -- French coach Hubert Velud disowned the tag of favourites before the first leg.
He insisted the title-decider in the African equivalent of the Europa League was a "50-50 affair" after two close-fought group games between the clubs.
Mazembe forced a 0-0 draw in Algeria last July and won the return match 1-0 thanks to a goal from Zambia captain Rainford Kalaba.
Bejaia began with nine Algerians plus Malian Soumaila Sidibe and France-born Chad international Morgan Betorangal.
Apart from four Congolese, Mazembe fielded three Zambians, two Malians and two Ivorians.
New Algeria coach Georges Leekens from Belgium was among a large, noisy crowd in the 37,000-capacity stadium as Bejaia dominated early territory and possession.
Mouloudia, competing in the Africa for the first time this year, had a chance to take the lead on 20 minutes when they got behind the Mazembe defence.
But Betorangal only got a timid poke at a low cross and goalkeeper Sylvain Gbohouo smothered the ball.
Mazembe went ahead on 43 minutes after sloppy defending by Sofiane Baouali allowed Roger Assale to break through and he was fouled by goalkeeper Chamseddine Rahmani.
Bolingi, the son of a former DR Congo goalkeeper, scored his fourth Confederation Cup goal of the season with a spot-kick into the corner of the net.
Yaya fluffed a chance to equalise early in the second half before levelling on 66 minutes with a free-kick that drifted over the defensive wall and high into the net.
A weak back-header by Salif Coulibaly seven minutes later offered Yaya a chance to score again, but he shot straight at the onrushing Gbohouo.