De Ketelaere opened the scoring at the Seattle Stadium in the ninth minute to cement Belgium's early dominance.
Malik Tillman equalised after 31 minutes when his free-kick hit Hans Vanaken and zoomed into the net past Belgium goalkeeper Thibaut Courtois.
But parity lasted only two minutes.
De Ketelaere headed in his second of the night past the US goalkeeper Matt Freese to send Rudi Garcia's men into the pause with a slight advantage.
The game was overshadowed by the decision ofWorld Cup organisers Fifa to suspend the one-match ban of the US forward Folarin Balogun.
The 25-year-old was permitted to play despite receiving a red card against Bosnia and Herzegovina after US President Donald Trump asked Fifa boss Gianni Infantino to review Balogun's punishment.
Balogun won the free kick which led to Tillman's leveller but otherwise failed to make an impact against a well-marshalled Belgium rearguard.
Blunder gives Belgium big advantage
After the restart, Freese effectively handed the game to the Belgians.
He came out of his penalty area to make a clearance but fluffed his kick allowing Vanaken to fire the ball into the ungarded net. Romelu Lukaku added the gloss in stoppage time.
The defeat means all three co-hosts are out of the 2026 tournament after Canada and Mexico lost their last-16 games to Morocco and England respectively.
Merino's late strike takes Spain past Portugal into World Cup quarter-finals
"In the moments that we were doing well in the tournament, we felt amazing," said US midfielder Tyler Adams. "And then obviously, an opportunity like today, we didn't."
Despite their exit, US head coach Mauricio Pochettino said the future was bright for the squad.
"I think now ... it's time to rest a little bit, to think, to have conversations, and then see what the decision is from the federation and from us," he said. "But I am so happy."
Ounahi stars as Morocco outclass Canada to advance to last eight at World Cup
On 10 July in Los Angeles, Belgium will take on Spain after they edged past Portugal 1-0.
Mikel Merino scored in stoppage time to decide the game in Dallas.
After the tie, the Portugal skipper Cristiano Ronaldo said he would not play in any more World Cups.
"I'll wake up tomorrow like I woke up today, with a clear conscience,” said the 41-year-old.
“I gave my best. I won three titles with Portugal. Before Cristiano, Portugal hadn't won any title. So, I'm happy. The biggest title that I won with the national team was in 2016 (European Championship), which for me had the same dimension as a World Cup, honestly.”


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