Uganda, who last played at the tournament in 1978, had already been eliminated before kickoff and the stalemate ended Mali's hopes of progressing from the Group D as Egypt and Ghana both went through.
Neither side had scored in their opening two games and the game produced 70 minutes of dismal football on a shocking surface before suddenly coming to life with two spectacular long-range goals within four minutes.
Uganda took a deserved lead when Farouk Miya collected ball just outside the area and fired a rising shot into the top corner.
Mali, five-times semi-finalists and once runners-up, quickly replied when 20-year-old Yves Bissouma scored with an even more impressive effort, a 30-metre free kick which flew into the net and left Robert Odongkara rooted to the spot.
The match, played in front of a sparse crowd which has become an unfortunate feature of the tournament, was preceded by a tropical downpour which left large parts of the pitch at the newly-built Stade d'Oyem under water.
The pitch deprived Uganda of their best first-half chance when Luwagga Kizito ran onto a through ball and got clear of the Mali defence, only for the ball to get stuck in pool of water before he could shoot.
Mali's best first-half effort was a Yacouba Sylla shot which he curled over the bar from just outside area as the players continued to splash around.
Uganda adapted better to the conditions in the second half and had a goal disallowed when Iceland-based Tony Mawejje's shot took a deflection off Kizito who was in an offside position.
That was followed by four minutes of excitement with the two goals before normal service was resumed with more misplaced passes and niggly fouls.
Egypt topped the group with seven points after their 1-0 win over Ghana on Wednesday, while the Black Stars were second with six points. Mali finished with two points and Uganda one.
(Writing by Brian Homewood in Berne, editing by Pritha Sarkar)
