By Michael Kahn
NATAL, Brazil, June 16 (Reuters) - A 2-1 win against a Ghana side that knocked the United States out of the last two World Cups will mean nothing if the Americans falter in their remaining Group G games, captain Clint Dempsey said on Monday.
The U.S. were beaten by Ghana in their final group stage game in 2006 and in the last 16 four years later.
"It just so happened we had history with Ghana," said Dempsey, who scored after 29 seconds on Monday but also suffered a broken nose.
"They pretty much knocked us out of the last two World Cups but this win means nothing unless we build on it."
The Americans hope they can carry the momentum into their next match with Portugal in Manaus on Sunday before taking on group favourites Germany in Recife as they bid to make the last 16 for the fourth time in the last seven tournaments.
A first step was finally beating Ghana and Dempsey's goal also marked sweet vindication for a player who helped lead the American attack in the two previous defeats against the Black Stars.
In 2006, the U.S. equalised when Dempsey scored late in the first half only for Ghana to convert a penalty minutes later to take a 2-1 lead that would send them through to the knockout rounds and the Americans home.
The Americans again fell behind in their last 16 match in South Africa in 2010 before Landon Donovan equalised from the penalty spot - only for Asamoah Gyan to split the U.S. defence in extra time and lash the winner past Tim Howard.
Despite their early lead on Monday, it looked like Gyan would once again help break American hearts when his sublime backheel set up Andre Ayew's 83rd minute equaliser after intense Ghana pressure.
A powerful header from substitute and World Cup debutant John Brooks three minutes later, however, gave the Americans their first win over their African rivals in three attempts.
"Any team you have beaten twice will come out very strong and I believe they came out very strong and they were determined not to lose a third time," Ghana coach Kwesi Appiah said. (Reporting by Michael Kahn, Editing by Justin Palmer)