Dala gave Angola the lead on the half hour in Bouake when a loose ball fell his way at a corner and his scruffy acrobatic effort bounced over two defenders on the line.
Sidi Bouna Amar hauled Mauritania level as he weaved through the Angola defence before producing an unerring low finish, but Dala responded with a goal of similar brilliance early in the second half.
Mauritania then paid the price for failing to clear, with Gilberto winning the ball inside the area and watching his shot deflect in off centre-back Lamine Ba.
Aboubakary Koita slammed in from 20 metres to raise Mauritanian hopes of a comeback, but Angola held on as Neblu made a crucial save to deny Amar a second of the contest.
Algeria in their opening match, ended a nine-game winless run at the tournament dating back to 2012 and took over top spot in Group D with four points.
They sit above Burkina Faso on goals scored and will secure a place in the knockout rounds with a draw against the Stallions in their final group fixture on Tuesday in Yamoussoukro.
Algeria, the 2019 champions, sit on two points after back-to-back draws, while Mauritania -- beaten by a stoppage-time Burkina Faso penalty on Tuesday -- are now without a win at the AFCON in eight attempts.
Amir Abdou's men must beat Algeria in Bouake next week to stand a chance of progressing as one of the four best third-placed nations.a