The Lions of Chinguetti might have picked up their maiden victory at the competition had Adama Ba buried a golden opportunity to score after an hour of a contest that saw Corentin Martins' men grow in confidence as it unfolded.
Mauritania went into the game still smarting from a 4-1 drubbing by Mali and their determination to run a tighter ship at the back paid off as they kept Angola's talented front four at bay, although they breathed a sigh of relief when Wilson Eduardo misfired with the goal at his mercy and a late Geraldo strike was correctly ruled out for offside.
The result leaves Angola with two points from two games and a strong chance of qualifying from Group E if they can get a result from their final game against Mali.
Meanwhile, Mauritania will need another gritty performance as they attempt to get something from their clash with Group E favourites Tunisia.
Djalma headed narrowly wide from Bruno Gaspar's cross and the Alanyaspor forward's pace caused Mauritania problems as Angola dominated the first half.
Fredy Ribeiro's clever pass played Gaspar in for a shot at goal from close range but he hesitated and fluffed his lines, while Mauritania threatened through Bakary N'Diaye, who headed straight at Tony Cabaca after rising to meet Khassa Camara's free-kick.
Mauritania's best chance of the game fell to Ba after the interval. He met Ismael Diakite's fizzing cross from the right with a first-time shot that Gaspar did brilliantly to slide in and block with his legs.
Moments later Angola squandered an even better opportunity when Gelson Dala burst into the box and pulled the ball back to substitute Eduardo but the Sporting Braga forward scuffed his shot and sent the ball wide to the left of the gaping net.
Geraldo thought he had won it when he volleyed Paizo's cross into the net at the far post in stoppage time, but an offside flag was correctly raised against him and Mauritania breathed a sigh of relief before celebrating a historic result.