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The Turkey-based striker took advantage of his first scoring opportunity to beat Aymen Mathlouthi after 14 minutes in the Mediterranean resort.
Aboubakar had several other chances, including a one-on-one with the goalkeeper, but could not add to his tally.
Tunisians Taha Yassine Khenissi and Syam Ben Youssef were foiled by the woodwork during the first half.
Aboubakar came off the bench to snatch a late winner against Egypt in the Africa Cup of Nations final in Gabon last month.
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He was one of two changes for the Tunisia match from the team that started the final, replacing Robert Ndip Tambe in the lone-striker role.
Midfielder Andre-Frank Zambo Anguissa was the other newcomer, winning his first cap in place of Sebastien Siani.
Anguissa was among eight players who withdrew from the preliminary Cup of Nations squad, preferring to concentrate on his club career with Marseille.
Belgian coach Hugo Broos kept a promise not to hold grudges against the "rebels" by including Anguissa and Schalke striker Eric-Maxim Choupo-Moting for two friendlies.
Cameroon play Guinea near Brussels next Tuesday ahead of Cup of Nations and World Cup fixtures from June.