The Black Stars captain handed his side the lead in the 21st minute when he headed home a Jordan Ayew cross and 2015's losing finalists successfully held on for the remainder.
Avram Grant's men had every reason to be confident heading into the encounter as the only team to have reached the semi-finals in each of the last five AFCON tournaments, having also won their Group D opener against Uganda 1-0.
Mali, on the other hand, recorded a scoreless draw against Egypt on matchday one and had set their sights on another surprise result in Port-Gentil.
But it was all Ghana before the break, although Gyan's goal was their only reward for a dominant display.
Mali improved in the second half as they went in search of an equaliser, but it was not enough to really worry leaders Ghana, who top their section with six points from two games ahead of the match against Egypt, with Mali on one point heading into their clash with Uganda on Wednesday.
Ghana dominated proceedings early on with Andre Ayew wasting two good chances, firstly heading wide when unmarked following a corner from Jordan Ayew before firing off-target from close range after good work from Christian Atsu down the right.
Grant's men continued to push for the opener and they eventually got the goal they deserved midway through the first half.
Jordan Ayew did well to skip away down the right after collecting a long ball, then sent in a pinpoint cross for Gyan who beat goalkeeper Oumar Sissoko with a fine header into the bottom-left corner.
Mali, meanwhile, struggled to create any chances of note in the opening 45 minutes with Molla Wague's header over the crossbar their only dangerous moment before the break.
Alain Giresse's side improved after the break and could have restored parity in the 52nd minute via Moussa Marega, the attacker wildly blasting a shot over the crossbar from a difficult angle after some good work from Bakary Sako.
Mali pinned back Ghana in their own half as they went in search of an equaliser and Hamari Traore almost made it 1-1 with what would have been a contender for goal of the tournament, the left-back hammering a volley narrowly over the top-left corner from 25 yards.
Mali refused to give up and substitute Kalifa Coulibaly was next to threaten when he diverted Moussa Doumbia's shot goalwards but goalkeeper Razak Brimah was on hand to deny him, before frustrating Sako deep into stoppage time as Ghana secured their spot in the last eight.