Angola, who claimed their biggest ever Cup of Nations finals win, had an early setback when goalkeeper Neblu received a red card and they were under pressure from a Namibia side that looked the most likely to find the net.
But the game turned when Gelson opened the scoring after 38 minutes.
Namibia defender Lubeni Haukongo received a red card shortly afterwards and the Angola forward completed his double from the resulting free-kick.
Angola added a third goal through Mabululu in the second period and now await a quarter-final tie against the winners of the last-16 clash between Nigeria and Cameroon that will be played later on Saturday.
Namibia made their debut in the Cup of Nations knockout rounds but could not profit from an early piece of good fortune.
Angola were reduced to 10 men after 17 minutes when Neblu handled the ball outside the box as he stopped Bethuel Muzeu’s chipped shot.
It was poor play all round by the team as defender Kialonda Gaspar was caught in possession by Muzeu, who had a clear run on goal and forced the error from the keeper.
Deon Hotto’s resulting free kick from the edge of the area was superbly saved by replacement keeper Antonio Dominique.
Despite their numerical disadvantage, Angola took the lead with a superbly constructed goal. Fredy was played into space on the right-hand side of the box and his low cross provided a tap-in for Gelson.
Two minutes later and it was 10 players each as Namibia defender Haukongo received a needless second yellow card and was sent off.
From the resulting free kick, the same two players combined for Angola’s second goal. Fredy delivered the set-piece and Gelson headed home for his fourth goal of the tournament.
Peter Shalulile fired over early in the second half as Namibia tried to reduce the deficit but it was Angola who scored the next goal.
Mabululu burst into the box after a quick counter-attack and curled a fine finish in at the far post to kill the contest.
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