The Rennes midfielder put Cameroon ahead before Geremi Njitap doubled the advantage in the first-half.
Tunisia managed to make a remarkable comeback through Chaouki Ben Saada and Yassine Chikhaoui, forcing the game into extra time.
Mbia was on target two minutes into the first period of extra time to break Tunisia hearts.
Four-time winners Cameroon will face hosts Ghana in the semi-final on Thursday.
Chikhaoui should have put Tunisia in front after 10 minutes when he stole possession from Geremi and powered his way into the box.
He was unfortunate in his attempt as he blasted a powerful drive from a narrow angle that went just wide of the post.
A blunder by Tunisia keeper Hamdi Kasraoui gifted Cameroon the opener in the 19th minute.
The Esperance guardian failed to handle Alexandre Song's left-wing cross, allowing Mbia to head into an empty net at the far post.
Geremi extended the lead just nine minutes later when he curled a superb free-kick over the wall and into the bottom of the net.
Despite going two down, the Carthage Eagles never gave up.
Ben Saada narrowed the gap in the 35th minute through another set-piece. He curled a left-footed free-kick past Carlos Kameni, who should have done better to palm away the ball.
The Espanyol guardian made amends four minutes before the break after producing a superb reflex save to deny Tunisia the equalizer.
Francileudo dos Santos cracked a thunderous shot from inside the box that stuck the bar. Ben Saada hit a low shot on the rebound but Kameni brilliantly blocked it on the goal-line.
Chikhaoui drew Tunisia level nine minutes from time, thanks to some neat work from substitute Saber Ben Frej down the right flank.
The Etoile Sahel man robbed Mohammadou Idrissou before providing a low cross to Chikhaoui, whose first-timer went past Kameni.
Mbia notched the decisive strike for Cameroon in the 92nd minute after side-footing Joel Epalle's flick-on into the back of the net.