Wakaso came on for Albert Adomah just after half-time and he broke the deadlock with a 54th-minute penalty before ending the fairytale run of the islanders with another goal deep in stoppage time.
His second effort came from a breakaway after Cape Verde keeper Vozinha had gone up field for a setpiece in desperate search for an equaliser.
Lucio Antunes, Cape Verde's charismatic coach who will now return to his day job as an air traffic controller, told reporters: "We cannot complain about the referee's decisions... we did not complain in our first three matches.
"But while I respect his country, is it right that a referee from Mauritius should be in charge of such a big match as an African Nations Cup quarter-final?"
"We have just watched a beautiful game of football but the best team lost. The best team in the competition is now going home so the tournament will lose a little of its shine," said the Cape Verde coach.
"But I congratulate Ghana. Although we were the better team they got the goals so it was a fair result. And really, who would want to see a semi-final between Togo or Burkina Faso and Cape Verde? There would be 200 people there.
"The tournament needs big teams like Ghana at the end," added Antunes.
"We expected a difficult game and Cape Verde certainly gave us one," said the striker. "They are tactically disciplined and get behind the ball well.
"The first half was a bit frustrating and they played better than us in the second half but the penalty was the key to winning. It put us on top and opened up the match.
"Now we have to correct our mistakes and improve for the semi-final," added Gyan who is hoping his side can land the title for the first time in 31 years.
The introduction of Wakaso, who was suspended for Ghana's game against Niger on Monday, certainly had an impact.
