Ghana will face hosts Equatorial Guinea in the semi-final of the 2015 Africa Cup of Nations on Thursday.
The four-time champions beat Guinea 3-0 in Sunday's third quarter-final clash to reach the last four for a fifth consecutive time.
The Black Stars took a 2-0 first half lead with goals from Christian Atsu and Kwesi Appiah and after the break Atsu scored a stunning goal to seal victory.
The host nation were trailing 1-0 to Tunisia deep into injury-time when referee Rajindraparsad Seechurn of Mauritius awarded them a penalty after Ivan Bolado tumbled in the box under the slightest of challenges.
Javier Balboa converted to take the game into extra-time.
It had already been a bad-tempered affair, not assisted by Tunisia’s rotational fouling [41 in all] and time-wasting.
It meant they failed to capitalise on the 70th minute lead given to them by Ahmed Akaichi’s neat finish.
There could be no criticism of the winner, however.
Balboa curled in a 25-yard free-kick and EG held on for the final 18 minutes of extra-time as the game degenerated.
At the final whistle, the Tunisian bench and substitutes surrounded the referee who had to be ushered from the pitch by armed security as EG fans began wild celebrations.
EG are ranked 118 in the Fifa rankings, 94 places below Tunisia.