The Carthage Eagles were held in check by the visiting West Africans and had to wait for almost an hour to break the deadlock.
Central defender Abdennour headed home from Ali Maaloul's corner on 58 minutes before German-born Ben-Hatira sealed victory with the second goal on 80 minutes. Ben-Hatira was at the receiving end of a long pass from Hamza Lahmar, and let in a spectacular shot from his left that beat Guinea goalie Naby Yattara.
Tunisia trail DR Congo who beat Libya 4-0 in the other Group A match with lesser goals despite both having three points apiece.
Elsewhere in Blida, visiting Cameroon came from behind to snatch a vital point off Algeria in their Group B fixture. 'Les Fennecs' took the lead after only seven minutes through El Arabi Soudani who notched home from close range.
The Indomitable Lions responded through captain Benjamin Mounkandjo on 24 minutes with a shot through the legs of Algeria goalie Rais M'Bolhi, after Edgar Salli put him through.
However, Cameroon had goalkeeper Joseph Ondoa to thank for keeping the scoreline intact after Islam Slimani early in the second half and Adlanre Guediora six minutes from time.
Nigeria's Super Eagles sit at the top of Group B after beating Zambia 2-1 away in Ndola. Cameroon and Algeria follow in that order with a point each with Zambia at the depth with no point.
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