Depu broke the deadlock after 43 minutes and put his side further in the lead with a second goal on 62 minutes.
Milson then sealed the win with his goal with nine minutes of the match remaining.
Angola headed into the encounter as defending champions, having beaten Namibia 5-0 at the Nelson Mandela Bay Stadium last year.
Both teams started this tie well, although it took until the 24th minute for the first real chance as Ime Okon's header came crashing back off the crossbar.
The Sable Antelopes were not to be overrun and held their own for the remainder of the first period, before scoring a timely goal just two minutes from half time through a Depu header from a well-struck set-piece.
Okon came agonisingly close to an equaliser at the start of the second half, but somehow contrived to drag his shot wide of the target.
Angola though were putting pressure on South Africa and were full value for their second goal when Depu stole in from close range.
Boitumelo Radiopane was denied by Dominic with 68 minutes played but it was Angola who were to end the tie the stronger of the two teams, as Milson fired home a superb free-kick from the edge of the area.