Captain Khazri, whose previous clubs include then-top flight Sunderland, levelled off a deflected free-kick on 70 minutes after Diadie Samassekou had put Mali ahead on the hour.
Mali top a group based at the Suez Army Stadium in northeastern Egypt with four points, Tunisia have two, Angola one and Mauritania are pointless.
Angola play Mauritania Saturday and if they win there is a strong likelihood that they, Mali and Tunisia will all make it to the second round.
Group winners and runners-up automatically qualify and will be joined by the best four of the six third-place teams.
Tunisia coach Alain Giresse reacted to a blunder from goalkeeper Farouk Ben Mustapha that gifted Angola an equaliser in a 1-1 draw this week by replacing him with Hassen Mouez.
The Mali line-up included forward Moussa Djenepo, who joined Premier League club Southampton this month from Standard Liege in a $19 million (16.7 mn euro) deal.
Mali stunned 1994 hosts Tunisia 2-0 in the only previous Cup of Nations match between them with then-president Ben Ali so angered by the home side that he left the ground at half-time.
After taking heavy media and public criticism for the lacklustre showing against Angola, Tunisia began impressively in their second group outing.
Captain Khazri struck the crossbar from an angled fifth-minute free-kick on the edge of the box in 36 degree celsius (96 fahrenheit) heat cooled slightly by a strong sea breeze.
Khazri spotted Mali goalkeeper Djigui Diarra off his line soon after and struck the ball goalwards from the centre circle, forcing the shot-stopper to save at the expense of a corner.
Mouez badly misread a free-kick just past the half hour, allowing the ball to fly between his raised arms, and then fell to the ground injured.
Khazri was not far off target with a shot from just inside the box after the perseverance of Taha Yassine Khenissi created the opening.
Diarra displayed bravery in one-on-one situations to foil Ellyes Skhiri and Anice Badri, who were both yellow-carded for overly physical challenges.
The stalemate was finally broken on the hour when Mali took the lead against the run of play as Mouez allowed an inswinging Samassekou corner slip between his hands into the net.
Tunisia recovered to level on 70 minutes from another set-piece as a Khazri free-kick was deflected by Moussa Marega past Diarra into the corner of the net.1/1 Mali’s players celebrate their opening goal during the 2019 Africa Cup of Nations (CAN) Group E football match between Tunisia and Mali at the Suez Stadium on June 28, 2019.
AFP
