In an otherwise miserable World Cup for Africa which lost five of its six sides in the first round, the "Black Stars" beat the United States 2-1 in a tight and pulsating encounter.
Ghana's win matched the feat of Cameroon in 1990 and Senegal in 2002 who also went to the quarter-finals.
The Ghanaians danced for joy at the end, as ecstatic fans trumpeted vuvuzelas in Rustenburg's Royal Bafokeng stadium.
In a repeat of the score when they met in Germany four years ago, Kevin-Prince Boateng drove home Ghana's first early in the game before Landon Donovan replied with a second-half penalty.
Then in extra-time, Asamoah Gyan ran on to a high ball, shrugged off a challenge and fired into the back of the net for a winning goal that will never be forgotten in Ghana.
"I am the happiest man in the world," Gyan said. "God has made me one of the best players in this tournament."
U.S. coach Bob Bradley lamented a "stinging, tough defeat."
URUGUAY'S PARTY
For former champions Uruguay, who won the trophy way back in 1950 and 1930, a 2-1 win over South Korea on Saturday put them in the quarter-finals for the first time in four decades.
Now they are hungry to go further.
"There are only 3 million people in Uruguay and we waited a long time for this," said thrilled coach Oscar Tabarez.
"Here's hoping the party goes on!"
Uruguayan striker Luis Suarez slotted in an easy first goal after Korean goalkeeper Jung Sung-Ryong was caught hopelessly out of position by an angled Diego Forlan cross.
The Asians fought back with spirit and equalised in the 68th minute through Lee Chung-Yong, but as torrential rain swept the lakeside stadium, Suarez swerved in a brilliant winner 10 minutes from time to spark jubilation back home.
"I was tired of hearing my grandparents always talk about 1950. Now it is our turn to celebrate and we are going to be champions for sure," shouted Laura Silva, 22, running between cars in the capital Montevideo, waving a big national flag.
The result confirmed the South American dominance that has taken all their five teams into the knockout stage.
Passion in Chile over their passage to the last 16 even overflowed into a riot, police firing tear gas and water cannon at rowdy fans throwing flags and bottles among 50,000 people who poured onto the streets on Friday night.
FRENCH WARNED
Only Japan are now still in from Asia.
For Europe, after the embarrassing first-round exits of France and Italy, just six teams remain out of 13 starters.
Upcoming fixtures include a needle match between old rivals Germany and England on Sunday for which police are beefing up security in the central city of Bloemfontein.
