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.
Ghana cleared their lines and Wakaso ran almost 60 metres as chasing defenders tried to catch him before he slid the ball into the empty net.
The Ghana players and supporters went wild with delight at the Nelson Mandela Bay Stadium after their side had been given a stiff test by the islanders, featuring in the finals for the first time and the smallest nation to play in the tournament.
The one moment of controversy came when the penalty was harshly awarded by referee Rajinjapasad Seechurn of Mauritius.
He ruled that defender Carlitos, whose cousin Nani plays for Manchester United, had felled Ghana skipper Asamoah Gyan with an unfair shoulder charge as they challenged for the ball.
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?"
Antunes, a close friend of Real Madrid coach Jose Mourinho, summed up the match in a manner not unfamiliar to the outspoken Portuguese.
BEAUTIFUL GAME
"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.
Gyan said the penalty proved to be the turning point in the match.
"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.
He made no mistake with his penalty, lashing the ball down the middle while keeper Vozinha leapt to his left.
Cape Verde tried to ral
