Diadie Samassekou put Mali ahead on the hour with an inswinging corner which Tunisia keeper Mouez Hassan tried to catch but, possibly caught out by a gust of wind, he allowed the ball to slip through his hands and into the net.
Khazri, who also hit the post in the fifth minute, levelled 10 minutes later when his free kick took a wicked deflection off a player in the Malian wall and completely wrong-footed goalkeeper Djigui Diarra.
Tunisia's second straight 1-1 draw left them with two points in Group E while Mali have four after beating Mauritania in their opening game.
It was a typically dour performance from Tunisia, whose coach Alain Giresse was facing a side he led in two previous AFCON tournaments. However, with debutants Mauritania to come in their final match, they should still reach the last 16.
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Mali, who face Angola in their final game, did enough to show that they could be one of the tournament's dark horses with forward Moussa Marega giving a tireless performance in attack despite the searing heat.
The Porto player managed to get in a shot before halftime despite being surrounded by six opponents, and was twice close to grabbing a late winner.
He sent one header over the crossbar and, after running onto an incisive through ball, was denied when Hassan managed to block his shot with his body, atoning for his earlier mistake.
The pace picked up as the sun went down late in the game and Amadou Haidara also had a late chance for Mali but shot straight at Hassan from the edge of the area after a good run by Adama Traore.
(Writing by Brian Homewood; Editing by Toby Davis and Christian Radnedge)
