After a slow first half in Fortaleza, the Group G encounter came alive when Mario Gotze bundled home Thomas Muller's perfect cross six minutes after the interval.
Ghana turned the match around with two goals in nine minutes shortly afterwards, Andre Ayew claiming his second goal of the tournament with a fine header, before Gyan's clinical finish made it 2-1.
Germany coach Joachim Low then introduced Miroslav Klose off the bench, and the Lazio veteran became the joint-highest goalscorer in FIFA World Cup history by prodding home at the far post, his 15th finals goal moving him level with Brazilian legend Ronaldo.
After their disappointing 2-1 defeat at the hands of the United States first time out, Gyan was delighted with his side's performance against a strongly fancied Germany outfit.
"I congratulate the team, we believed in ourselves against a strong side like Germany," he told BBC Sport.
"It was a fair game. Tactically we were perfect, we had to stay back and wait for them because they are good in possession and we don't want to waste our energy running around after them.
"I was just waiting for my chance to happen. I had a couple of chances in the first game so I was a bit nervous and more focused today."
Appiah, meanwhile, felt his side could have taken all three points had they not squandered the opportunities they created.
"Our boys did well matching them," he said. "We created a lot of chances that we could have taken but we could not utilise them.
"They were really determined to fight to the end, it's just unfortunate that it ended this way but on the whole it was a very good game."
