(CNN) -- The United States crashed out of the World Cup on Saturday night as Ghana became just the third African team to ever reach the quarterfinals with a 2-1 extra-time victory.
Asamoah Gyan scored the winning goal in the third minute of the opening period of non-regulation play as Ghana's "Black Stars" eliminated the U.S. for the second time in a row at soccer's showpiece tournament.
Ghana will now play Uruguay in the last eight in Johannesburg on Friday, after the South Americans defeated South Korea 2-1 earlier on Saturday.
"I am the happiest man in the world. In 2006 we made the second round, now we have gone a step further. We have made Ghana proud and the whole of Africa proud," Gyan told reporters after his side followed in the footsteps of Cameroon in 1990 and Senegal in 2002.
U.S. coach Bob Bradley lamented his side's failure to match their opponents' strength.
"I thought at 1-1 we had a chance, but we didn't have enough freshness against all of Ghana's power," he said. "We have a great squad. We're proud but also disappointed not to have gone further."
Kevin-Prince Boateng put Ghana ahead in just the fifth minute of the second-round tie in Rustenburg as the U.S. paid for losing possession, but Landon Donovan leveled the scores with a second-half penalty.
The Ghanaians, who beat the U.S. 2-1 in the final group game at Germany 2006 before losing to Brazil, are the only Africans left at the first World Cup to be held on the continent.
Midfielder Boateng, who switched nationalities before the tournament after representing Germany at under-21 level, pounced to score the opening goal with a clinical left-foot finish after Ricardo Clark lost the ball near the halfway line and allowed him to surge towards the U.S. goal.
Bradley quickly responded to his team's predicament by hauling off Clark on the half-hour mark, bringing on Maurice Edu.
It was another substitution that sparked the Americans into life, as Benny Feilhaber again impressed after coming on at halftime for the third successive match.
The midfielder forced a close-range save from Ghana goalkeeper Richard Kingson as his introduction freed up Donovan and Clint Dempsey.
That duo combined to bring the U.S. level in the 62nd minute when 19-year-old defender Jonathan Mensah was booked for bringing down Dempsey, allowing Donovan to net his 45th international goal from the penalty spot and become the Americans' overall top scorer at World Cups.
Kingson then did well to block Michael Bradley's low shot, and Jozy Altidore fluffed his effort wide of the Ghana goal under pressure from the elder -- and unrelated -- John Mensah as the U.S. could not repeat their heroic late efforts from previous matches.
The Americans were caught napping again soon after the restart as Gyan out-muscled captain Carlos Bocanegra to get to Andre Ayew's punt forward and fire past goalkeeper Tim Howard.
It was his third goal of the tournament after scoring twice from penalties as Ghana qualified second from Group D behind Germany following a tense final round of matches that saw three teams level on four points.
The U.S. poured forward desperately in search of an equalizer, but could not force the tie into a penalty shootout.
Ayew will miss the quarterfinal at Soccer City along with the younger Mensah as both received their second bookings of the tournament during regulation time.
Donovan and Gyan top the overall goalscoring charts along with Uruguay striker Luis Suarez, Argentina forward Gonzalo Higuain, Spain star David Villa and Slovakia's Robert Vittek.