Abu Iddrisu put Ghana into the driving sea after about nine chances that fell for the Starlets had been wasted within the first 40 minutes.
In the 42nd minute, Baba Sule doubled the lead when he headed the ball home before Awudu Issaka scored the first of his three to begin his historic mission.
Issaka Issaka danced his way through the Tunisian defence and in the process scored twice.
And Charles Alloyed recorded the 6th goal before Emmanuel Bentil atoned for his earlier misses with the goal.