The Black Princesses won 1-0 in regulation time to tie the game at 1-1 after losing the first leg a fortnight ago.
Beatrice Sesu scored in the 17th minute to give Ghana the lead before the game traveled into penalties.
However, during penalties, the Black Princesses secured a hat-trick of World Cup qualifications as Fatima Alhassan scored the decisive kick at the Accra Sports Stadium.
In qualifying successfully, Ghana join Nigeria as the continent’s two representatives for the tournament to be hosted by Canada in August of this year.
The World Cup will be played between 5th and 24th August.