Ghana advanced to the last 16 as winners of Group F ahead of defending champions Cameroon. Tunisia were second in Group E with three points from three draws.
Ayew, 29, and his younger brother, Jordan, contributed three of Ghana’s four goals in the pool stages..
"We have watched them, know how they play and are going to beat them," added Ghana midfielder Mubarak Wakaso. "We are taking this tournament match by match, never looking beyond our next opponents. Our focus in exclusively on defeating Tunisia and reaching the last eight."
Tunisia’s form in the group stages was patchy. But coach Alain Giresse said those matches were now irrelevant and pointed to the elimination of Egypt and Morocco – two sides who won all their games in the group stages.
"A couple of big teams are out of the competition. That opens it up for everyone,” said the Frenchman. “It’s true that we have to improve our ability to create chances. We have to be even more committed and focused.”
Tunisia have not lifted the continental title since 2004. Ghana have been waiting since 1982 to hoist the crown for a fifth time.