Haidara rifled home from outside the penalty area in the 37th minute as Mali, one of the tournament's dark horses, set up an intriguing knockout-round clash with neighbours Ivory Coast.
The Malians, already qualified, finished Group E with two wins and a draw from their three games. Angola ended up third with two points, which was not enough to take them through as one of the best third-placed teams.
Angola, who scored one goal in three games, had plenty of possession and created several openings but their attack lacked punch. Tunisia took second spot with three points after a 0-0 draw with bottom side Mauritania, who finished with two.
South Africa finished with three points in their group and qualified along with Benin, Guinea and Democratic Republic of Congo as the best third-placed teams.
"We had several chances in the first half and, against Mali, you don't have the right to miss those chances," said Angola coach Srdjan Vasiljevic.
"Before the match, we calculated that we were going to have two or three chances to score. That was the case but unfortunately we didn't make the most of those chances."
Gelson Dala breached the Mali defence but shot straight at goalkeeper Djigui Diarra in the fifth minute, a miss that Angola would later regret.
Mali, who rested several regular starters including forward Moussa Marega, fired their first warning with an Adama Traore shot which Toni Cabaca turned away for a corner before Haidara broke the deadlock.
He collected a pass from Moussa Doumbia outside the area, took one stride forward and thumped a rising shot into the goal from 25 metres.
Angola created plenty of openings in the second half but were let down by a poor final pass.
Gelson Dala had the best effort when he ran at the heart of the Mali defence and slipped past his marker but sent his angled shot just wide of the post.
"We are a young team with a lot of potential," said Haidara. "We have played together for a long time, we developed together. We wanted to win the group; now we have to concentrate on the next match."
(Writing by Brian Homewood; Editing by Ken Ferris and Clare Fallon)
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