Mali will play Senegal in the last eight.
Mali stunned Tunisia in the Africa Cup of Nations, prevailing in their last-16 tie in a penalty shootout despite playing much of the game with 10 men.
Tunisia were the favourites to reach the last eight and set up a meeting with Senegal, who overcame Sudan 3-1 earlier on Saturday.
They entered the game winless in four AFCON meetings with Mali, but their hopes received a huge boost when Woyo Coulibaly was sent off for a rash challenge on Hannibal Mejbri in the 26th minute.
Tunisia struggled to make their extra man count, and there were no shots on target for either team in a game that lacked quality until the 78th minute.
But it looked as if Tunisia had sealed a place in the last eight when Firas Chaouat headed them into a 88th-minute lead.
Yet there was a dramatic twist in injury time as Yassine Meriah was ruled to have handled in the area, giving Mali talisman Lassine Sinayoko the chance to draw them level from the penalty spot.
He promptly did so with his third goal of the tournament, and Tunisia were unable to find a way through the Mali defence for a second time in the subsequent 30 minutes of extra time.
Tunisia twice surrendered the advantage in the shootout, and Mohamed Ali Ben Romdhane’s miss with their fifth spot-kick enabled Bilal Toure to seal a famous triumph for the Eagles in Casablanca.
