As the clocked ticked down to halftime, Kingson pushed out Bastian Schweinsteiger's free kick.
Seven minutes after the restart, Ghana's Kwadwo Asamoah broke down from the middle and with just Neuer to beat, he fired into the keeper's legs.
A draw would send the two sides into the second round but neither looked like playing for a tie.
The deadlock was broken in the 62nd minute as Mesut Oezil smashed a left-footed shot into the top corner of the net from the edge of box.
Ghana went all out for an equalizer and they almost did it when Ayew burst into the box and shot from close range, but Philip Lahm's legs deflected it over the bar.
Germany, who have never failed to move beyond the first group round of the tournament, will next take on old foes England.
Germany coach Joachim Loew admitted England would be a handful but he believed his side would emerge winners.
"England are stronger than Ghana but I believe we will beat them," he said.
Australia are heading home despite a 2-1 victory over Serbia in Nelspruit.
Tim Cahill and Brett Holman put the Socceroos 2-0 up before Serbia pulled one back through Marko Pantelic at the 84th minute.
In a make-or-mar match for England, held in Port Elizabeth, Fabio Capello's side broke the hearts of Slovenia, who dropped from first place to nowhere.
In the 14th minute, Frank Lampard tested Samir Handanovic with a long-range free-kick. The winner came 12 minutes later as James Milner swung in a ball from the right and Defoe got there ahead of Marko Suler to volley into the roof of the net.
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2020-09-15
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