Wakaso struck twice in the second half, once from the penalty spot, as Ghana clinched a semi-final meeting with Burkina Faso or Togo.
Ghana were fortunate to break the deadlock after 54 minutes at the Nelson Mandela Bay Stadium.
The referee, Rajinjapasad Seechurn of Mauritius, harshly ruled against the Cape Verde defender Carlitos as he and Asamoah Gyan went for the ball and the Ghanaian went tumbling to the ground.
Wakaso, who had replaced Albert Adomah seven minutes earlier, made no mistake from the spot as he lashed the ball down the middle while the goalkeeper Vozinha leapt to his left.
Cape Verde had a chance to equalise within a minute but Heldon’s shot went narrowly wide.
Platini also went close for the islanders when he was denied by an acrobatic save from Fatau Dauda who then did even better to deny Djaniny in the closing minutes.
Wakaso added the second goal from a Ghana breakaway in the last minute when he slotted the ball into an empty net after Vozinha had gone up for a set piece at the other end.
Earlier, there was nothing to choose between the teams in a first half in which both sides played some good football in midfield without producing a single shot on target.
Cape Verde, making their debut appearance in the Nations Cup finals, were far from overawed in the biggest game in their relatively brief international history.
The islanders had two excellent opportunities to take the lead in the opening 22 minutes. Heldon, who scored the winner in the 2-1 victory over Angola on Sunday, fired high and wide from the first and then thumped another chance way over the bar after some good build-up play.
Ghana, despite looking sharper on the ball and weaving some nice flowing patterns around the Cape Verde defence, lacked any incisive threat with the usually dangerous Gyan too much on the periphery.
That changed in the second half when Wakaso came into the midfield and livened things up.
His two goals kept alive Ghana’s dreams of a fifth title, 31 years after their last triumph in 1982.