Belgium required extra-time to claim a 2-1 win over a battling USA side and book a World Cup quarter-final date with Argentina.
An end-to-end encounter somehow finished goalless after 90 minutes, with Kevin De Bruyne and Romelu Lukaku eventually settling the tie despite Julian Green stepping off the bench to set up a grandstand finish.
The best of the chances in normal time fell to Belgium, with the clearest dropping the way of teenage striker Divock Origi who could have netted inside the opening 40 seconds and saw a looping header crash off the top of the crossbar.
The United States had their moments as an attacking force, but it was to be dogged defending and some inspired goalkeeping from Tim Howard that kept them in the contest.
They remained level for 93 minutes, but the introduction of Lukaku’s pace and power at the start of extra-time was to prove their undoing.
The Chelsea striker brushed aside Matt Besler on his way into the box and squared for former Stamford Bridge team-mate De Bruyne to work the ball onto his right foot and drill low across Howard into the bottom corner.
Lukaku then netted the second himself, racing onto a perfectly-weighted pass from De Bruyne to rattle a first-time effort past Howard at his near post.
The USA looked down and out at that stage, with physical and mental energy drained, but they somehow picked themselves up to halve the deficit through Green’s impressive volley and came agonisingly close in the dying stages to forcing a penalty shoot-out.
The statistics will tell a tale of Belgian dominance, but that will miss the story of American heroics.
From the first minute, Howard stood tall when Belgium's 19-year-old striker Origi caught Omar Gonzalez flat-footed and only the keeper's outstretched foot prevented his team going behind in the very first minute.
The USA confounded expectations by fielding an attacking formation rather than keeping things as tight as possible, and that nearly paid off when Michael Bradley linked up with Clint Dempsey but he could not find the power with a clipped shot to really test Thibaut Courtois.
De Bruyne was guilty of the most glaring miss of the half when he cut back inside but sent a tame shot rolling wide of the post.
He then tried to make amends with a first-time shot but Howard held it easily.
The second half began with Belgium looking threatening and the USA relying on fortune and Howard.
Dries Mertens' looping header was flicked over the bar by Howard, Jan Vertonghen's left-wing cross evaded both De Bruyne and Origi, then Origi sent in a good header which landed on top of the crossbar.
It was not all one-way traffic, however, and the Belgium defence made a hash of dealing with Damarcus Beasley's cross and Graham Zusi lashed in a shot that Vincent Kompany was fortunate to get in the way of.
Axel Witsel zipped a low shot not far off target before Howard once again came to the rescue to defy Origi, who would have been disappointed with his effort.
Dempsey had a shot on target as the USA tried to respond, but it was Howard saving with his feet again that kept the USA in the game. Howard was again inspirational when Kevin Mirallas' run saw Eden Hazard given a sight of goal, but the keeper parried.
Besler produced an astounding block to deny Daniel Van Buyten, before another Howard save saw the Everton keeper tip over Origi's rising drive.
With normal time running out, Kompany went close to bundling over the line, but Howard once again was equal to the challenge.
Chris Wondolowski could have snatched it for the USA but sliced horribly wide.
Belgium boss Marc Wilmots gave Lukaku a chance to make up for his disappointing tournament, on for Origi, and within two minutes of extra time starting he had made the goal.
Lukaku's strength and pace down the right opened up the USA and De Bruyne fastened on to the ball to fire in low at the far post with Howard for once beaten.
Mirallas, another Everton man, could have wrapped it up but another intervention by Howard kept it at 1-0.
That was only putting off the inevitable though as, with the USA looking done, De Bruyne this time played in Lukaku to fire home first-time at Howard's near-post.
The game seemed over, only for Green to pop up with a goal with just about his first touch, the 19-year-old Bayern Munich player beating Courtois with a volleyed finish to keep things interesting until the very end.