كتب : Hatem Maher
Nottingham Forest striker Junior Agogo scored the winner for the four-time African champions five minutes before the break.
Ghana top Group A with six points from two games, three ahead of Morocco and Guinea, who lie second and third respectively.
Namibia have no chance of progressing after suffering two consecutive defeats.
Ghana winger Quincy Owusu-Abeyie almost opened the scoring after 12 minutes when he gathered a loose ball at the far post but his weak shot was blocked by Namibia keeper.
Sulley Muntari had another golden opportunity in the 30th minute when a mis-timed jump by Namibia guardian Athiel Mbaha allowed him to head goalwards.
The Portsmouth man was unfortunate to see his header clips the far post and goes out.
Two minutes later, Asamoah Gyan horribly missed an open goal as the Ghanaians continued to suffer from their inability to score and break Namibia's resistance.
The Udinese striker had a chance to score into an empty net when the ball fell into his path after Mbaha blocked Laryea Kingston's close-range effort but he blasted wide with the goal at his mercy.
Ghana's pressure finally paid off in the 40th minute when Agogo converted Michael Essien's low cross from close range.
The Black Cats' form dropped in the second period, allowing Namibia to launch several threats.
Brian Brendell, who scored Namibia's only goal in the humiliating 5-1 defeat to Morocco, squandered a couple of clear-cut opportunities midway through the second-half.