With hosts Egypt beating Cameroon 2-1 in the other Goup A game, the Black Meteors finished second on the table behind The Pharaohs and just above the Indomitable Lions courtesy of a better goal difference after both sides finished on four points each.
Bottom-placed Mali, on the other hand, leave for Bamako with three straight defeats and without scoring a goal.
Ghana coach Ibrahim Tanko made one change to his line-up, replacing Owusu, who failed to live up to expectations in the first two games, with Dutch-born Robin Polley who was handed his first-ever appearance for Ghana at any level.
Mali started promisingly, forcing Ghana goalkeeper Kwame Baah into a double save in the seventh minute. The Kotoko man tipped Ibrahima Kone’s shot against the upright before pushing Boubacar Traore’s follow-up effort away.
After a few half chances for both sides, The Eagles went close again in the 35th minute when Kone headed a Moussa Bagayoko cross just wide.
Then Evans Mensah pounced on a loose ball in the box but his feeble shot was no problem at all for Mali goalkeeper Samuel Diarra.
In dire need of a win at all cost to stand a chance of making the next round, Ghana lifted their game in the second half.
In the 74th minute, Tanko’s outfit broke the deadlock through Owusu who rose high to head a Kingsley Fobi cross beyond Diarra.
Two minutes later, the Black Meteors went close to doubling their lead but Owusu failed to direct his close-range effort on goal after connecting a Michael Agbekpornu cross.
Six minutes to full-time, Mali went knocking at the Ghana goal but goalkeeper Baah did well to push substitute Diadie Samadiare’s shot away.
Ghana finally got their second goal in the 86th minute as Owusu beat Youssouf Traore to pounce on an Emmanuel Lomotey flicked effort and shoot past Diarra into the net.
Late in injury time, Mali had a chance to halve the deficit but Clement Kanoute could only scuff a close-range shot just wide as Ghana hung on to claim a famous 2-0 win.
In the other group game, two goals from Mohamed Moustafa earned Egypt a 2-1 triumph over Cameroon to finish top of the table. Eric Ayuk registered the Indomitable Lions’ consolation goal.