Ghana proved too strong for Namibia as the tournament hosts moved three points clear at the top of Group A.
Agogo (c) celebrates his goal against Guinea
After Asamoah Gyan shot over the bar with the goal gaping, Junior Agogo bundled in a Quincy Owusu-Abeyie cross from close range on 41 minutes.
But Namibia were not disgraced and had Brian Brendell showed a bit more calm on at least three occasions they might have snatched a surprise equaliser.
Collin Benjamin also missed chances for Namibia as Ghana closed out the game.
Ghana's two wins should take them through to the quarter-finals, though they need a draw against Morocco to be absolutely certain.
Henri Michel's Morocco, who were beaten by Guinea earlier on Thursday, will probably need to win to have any chance of qualifying in that final group game on Monday.
Sore from their 5-1 loss to Morocco, Namibia replaced goalkeeper Abisai Shiningayamwe with Athiel Mbaha.
The Brave Warriors were far more organised defensively this time, and they managed to soak up plenty of Ghana pressure early on.
On 19 minutes Namibia broke away and had an opportunity to take a surprise lead, but Brendell shot wide from the edge of the penalty area.
Ghana wasted their chances too, notably when Gyan failed to shoot into an open goal on 34 minutes, with the goalkeeper committed.
Agogo's goal came from the vision of Michael Essien, who was named man-of-the-match.
The midfielder laid on a pass inside the penalty area to Owusu-Abeyie, who found Agogo inside the six-yard box.
The finish was not elegant, but it was enough to delight fans in the packed stadium in Accra.
The first 20 minutes of the second half were tame, though Ghana remained in control.
But two more chances fell to Brendell mid-way through the second half, shooting wide after Namibia break, then firing over the bar a minute later.
Benjamin shot wide in the 75th minute from a Namibia corner kick, and he also missed a chance five minutes from time.
Ghana continued in search of a second goal, but faltered in the final third of the pitch.
Ghana winger Laryea Kingston picked up his second yellow card of the tournament, for taking a free-kick too early, and misses the match against Morocco.