Asamoah Gyan blasted in a penalty kick in the 84th minute after a handball by Serbian Zdravko Kuzmanovic, then joined in a dance-filled team celebration that saw even a security guard hug Gyan.
"Everyone is happy, not only in Ghana but the whole of Africa," Gyan said. "I'm so happy, not for Ghana winning but for an African team winning in the World Cup. It's not so easy. We knew all Africa would support us. I really drove off that."
Ghana coach Milovcan Rajevac, a Serbian, was excited his team could pull off the historic triumph after the hosts, Nigeria and Algeria had failed to bring the continent a FIFA World Cup triumph.
"This was the first time the World Cup was held on African soil and so I'm happy an African team beat a great European team and I'm happy that the whole of Africa is pleased about this win," Rajevac said.
Ghana was the only African team to reach the Round of 16 at the 2006 FFA World Cup, eventually losing to Brazil in the knockout stage, and the victory over Serbia has boosted the Black Stars' chances of advancing in 2010.
"It was big for Africa. It means a lot. We showed we could beat them," said Ghana midfielder Andre Ayew. "I don't know if this means we have arrived. Our dream is advancement."
Ghana captain John Mensah added: "We played with our hearts. We don't have to do anything else. It's beautiful. To win the first game out is very important. We're happy now. Tomorrow we will go back to working." Matches against Australia and the Germans now follow.
For Gyan, patience was critical in beating Serbia, in a game which saw Aleksandar Lukovic red-carded after a second yellow card 10 minutes before Gyan's goal.
"We knew what the Serbians were going to do," Gyan said. "We were patient and waited for them to make mistakes and that's what happened. It's not the first time I have taken a penalty in front of a huge crowd. There was no pressure on me."
Gyan said his team gives defence a greater priority than in 2006 and that has been a key to success. "Now we make sure we defend our goal before we attack," he added. "In 2006, we were attacking more without doing that."