In a game that was often scrappy and marred by a number of arguments between both sets of players over alleged stray arms and elbows, it was Goran Stevanovic's men who kept their cool and won through to a semi-final with Zambia thanks to Andre Ayew's 101st-minute goal.
When that came it was a gift from Tunisia goalkeeper Aymen Mathlouthi, who shelled Samuel Inkoom's cross into the striker's path.
Prior to that, John Mensah's 10th-minute header for Ghana had been cancelled out by Saber Khelifa before half-time. But on weight of chances Ghana deserved to win, with their route to the finish line eased by Aymen Abdennour's sending-off for an elbow on Ayew.
That incident, which came 18 minutes into extra time, caused the game to end on an unsavoury note - something which had looked unlikely when Mensah opened the scoring, heading in at the back post after Emmanuel Agyemang-Badu's corner was flicked into his path by Kwadwo Asamoah.
It could have been two shortly after when Agyemang-Badu nodded wide himself, before Tunisia had a penalty appeal rejected when Khelifa appeared to go down under the challenge of Inkoom.
Ghana striker Asamoah Gyan then worked Mathlouthi as his side looked for a second, but the next goal would go the way of Tunisia three minutes before the break, when Khelifa got his head on the end of Zouheir Dhaouadi's cross.
After a lively first half, the second took some time to get going, with Asamoah's hit wide on the hour the first real action.
Gyan's cross then saw Agyemang-Badu draw a save from Mathlouthi with a header, before Tunisia responded with a Youssef Msakni shot that was blocked by John Boye.
Ayew then had a drive tipped over as Ghana turned up the pressure, while the same player headed over and Gyan was denied by Mathlouthi's feet.
Jordan Ayew also worked Mathlouthi and, after the game entered an additional 30 minutes, it was unfortunate that the excellent Mathlouthi should be the villain.
He came for Inkoom's cross and, despite it seeming to be a routine take, he dropped it at the feet of Ayew and he did the rest.
Tunisia became ragged after that and Abdennour summed that up when he saw red, although his side could have forced penalties had Msakni shown better composure when free in the box.
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