Sabeur Khlifa got the faintest of touches to a free-kick from Khaled Korbi to open the scoring and a counter-attack finished off by substitute Youssef Msakni in the 77th minute ensured another upset result in the tournament co-hosted by Gabon and Equatorial Guinea.
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Morocco made a late charge in search of a draw with captain Houcine Kharja pulling a goal back in the 86th minute but then missing from close range in stoppage-time.
Tunisia allowed few opportunities to their North African rivals, one of the tournament favourites.
"Bravo Tunisia, they are our bette noire, we have not had much luck against them over the last decade," Kharja told reporters.
Khlifa's goal came against the run of play after Tunisia had rattled the Morocco woodwork on a rare counter-attack.
Morocco goalkeeper Nadir Lamyaghri misjudged the flight of Korbi's free-kick, distracted by Khlifa's effort to get his head to it.
Tunisia's second goal went perfectly to plan as Morocco surged forward and were caught on the break, competently finished by Msakni with a powerful low shot.
Kharja's goal ensured a late rally but Morocco looked too tired to grab a second.
"I think we deserved the win, we might not have made many chances but we defended superbly. I was surprised at the standard of our play," Tunisia coach Sami Trabelsi said.
In the earlier Group C match, Gabon easily beat Niger 2-0 in front of a rapturous home crowd.
