Mohamed Ali Moncer scored his first international goal for the North Africans, but the Blue Sharks found an equaliser through the industrious Almeida Heldon.
Cape Verde could have had the lead as early as the first minute when centre-back, Fernando Varela struck the woodwork with the goal gaping.
Tunisa's first real chance came in the 15th minute as Ahmed Akaichi found room in the box only for Josimar Vozinha to make a smart save low to his left.
The best chance of the half fell to the islanders as Heldon took advantage of a slip from AS Monaco man, Aymen Abdennour, but Jorge Djaniny fired a tame effort straight at Aymen Mathlouti.
The Carthage Eagles finally broke the shackles in the 70th minute. Moncer finished well at the back post following an impressive move down the right channel by Ali Maaloul.
But the tireless Heldon got some reward when he levelled from the penalty spot seven minutes later as the match ended in a tie.
With DR Congo and Zambia playing to the same scoreline it leaves the group wide open.
Zambia’s Given Singuluma struck first after an early error by Congo goalkeeper Robert Kidiaba in the remote town of Ebebiyin.
Congo equalised in the 66th minute when Yannick Bolasie swept a shot into the top left corner after the ball fell to him on the edge of the area.
The teams were the first at the competition to play at Ebebiyin Stadium, a 5000-seat ground hastily put together for the continental championship.
Local fans cheered both countries.