When Deivi 'Gilberto' Vieira gave the Angolans a two-goal lead on 72 minutes, his side looked set to win the Group D opener at the Olympic Stadium in the chilly western city of Oran.
But Yoro Diaby nodded a corner into the net six minutes later and substitute Coulibaly poked a loose ball past goalkeeper Hugo Marques to complete a dramatic comeback.
Laurindo 'Depu' Aurelio had twice put Angola ahead in the opening half with 36-year-old Hamidou Sinayoko scoring in between for Mali.
After only five goals in the first five mini-league matches at three other venues, the goal feast excited a small crowd on a winter evening in the 40,000-seat stadium.
Mali and Angola have both come close to winning a unique national team tournament as it is restricted to footballers playing at clubs in their country of birth.
Angola finished runners-up to Tunisia in 2011 and Mali lost the 2016 final to the Democratic Republic of Congo and were beaten by Morocco in the 2020 title decider.
After the drama of the opening match in a double-header, Cameroon defeated Congo Brazzaville 1-0 in Group E in a much less exciting central African showdown.
Cameroon, who came fourth as hosts of the last edition, always looked likely winners, but took 63 minutes to break the deadlock against dogged opponents.
When the ball was lofted into the goalmouth, Jerome Mbekeli dashed forward and his powerful, perfectly placed header gave goalkeeper Pavelh Ndzila no chance.
Substitute Mbekeli set up the only goal for Vincent Aboubakar when Cameroon shocked Brazil in a 2022 World Cup group match in Qatar last month.