After an entertaining 90 minutes ended goalless, Belgium netted soon after the restart through Kevin de Bruyne, before the former Chelsea midfielder turned provider to set up Romelu Lukaku for the second.
USA responded in the second half of extra time through Julian Green, but it wasn't enough to prevent Belgium from moving through to a last-eight encounter with Argentina.
Below, Sports Mole assesses whether Belgium were deserving of their place in the quarter-finals.
On target: 17
On target: 5
Was the result fair?
When a team creates 39 chances in a football match, you have to say that they deserve to win, but USA, who spent the majority of the match on the back foot, were extremely unfortunate not to force a penalty shootout. For what they lack in ability, they make up for in desire, and they have been a breath of fresh air in this tournament. However, Belgium finally showed in this match that they have exceptional quality within their ranks, and they will be fancied to topple Argentina in the quarter-finals.
Marc Wilmots's team have come in for criticism after their below-par performances during the group stages but the Belgium that turned up in Salvador was the team that have long been considered as the dark horses for this tournament. They miss a clinical touch in attack, but in the likes of De Bruyne, Eden Hazard and Kevin Mirallas, they have some of the outstanding talents in world football. De Bruyne deserves particular credit after yet another tremendous showing, and his goal and assist for the second were the decisive factors in this match.
USA have never argued that they possess the same ability as some of the teams in Brazil, but it's difficult to find a team who displays as much heart as Jurgen Klinsmann's side. From start to finish, they ran themselves into the ground, with several players visibly exhausted with more than a quarter of normal time remaining. Goalkeeper Tim Howard acted as the main rearguard as Belgium tried to pummel them into submission, but Howard and his teammates responded to push their opponents to the brink.
Sports Mole's man of the match
Tim Howard: He may have ended the night on the losing side, but Howard will be seen as a hero back in the United States. The Everton goalkeeper produced a stunning display as Belgium peppered his goal for the duration of the second half of normal time. He was finally beaten by De Bruyne, but the 35-year-old is now the holder of the record for the highest number of saves in a World Cup match.
This accolade can only go to one of the referee's assistants, who wrongly adjudged that Chris Wondolowski had drifted into an offside position deep into added-on time at the end of the second half. The assistant was fortunate because if Wondolowski, who was a yard onside, had converted the simple chance, he would have cost USA a place in the last eight.
Klinsmann had his concerns about Djamel Haimoudi before the start of this match, but he needn't have done after the Algerian official delivered another display of the highest order. He was quick to clamp down on any misdemeanours from either side while he applied common sense to a number of incidents that occurred during the 120 minutes.
Belgium: Belgium move through to quarter-final showdown with Argentina, with the winners of that tie facing France or Germany in the last four.
USA: Despite suffering defeat in Salvador, USA will head back home to widespread praise from a country who are still trying to fall in love with the sport.