Higuain struck in the eighth minute at the Mane Garrincha National Stadium to send Argentina into the last four for the first time since 1990 and thwart Belgian hopes of avenging their defeat in the 1986 semi-finals.
Alejandro Sabella’s side will play either the Netherlands or Costa Rica, who face off in the fourth and final quarter-final later on Saturday.
The only black mark for Argentina was an injury to influential midfielder Angel Di Maria that forced him off in the first half and may yet deny him a chance to play in the semi-final.
“It was our best game of the World Cup,” said Sabella.
“It is a great joy for this team, for the people for my family and for everyone. This was the best game for Argentina in terms of balance and all aspects of its game.
“However, the injury to di Maria is a big blow.”
Hours after Neymar was ruled out of the tournament due to injury and James Rodriguez was eliminated with Colombia, Lionel Messi gave further evidence to suggest the World Cup may yet belong to him.
He illuminated Argentina’s play with his trickery and incisive passing and although he failed to score, Higuain’s goal was enough to see off Belgium’s ‘golden generation’, for whom the occasion proved a step too far.
A symbol of Belgium’s travails, star player Eden Hazard was booked for a crude challenge on Lucas Biglia and then replaced by Nacer Chadli with 15 minutes remaining.
Showing three changes to the team that had laboured to beat Switzerland in the last 16 — Jose Maria Basanta, Martin Demichelis and Biglia coming in — Argentina were quick to put Belgium on the back foot.
Messi was at the forefront, freeing Ezequiel Lavezzi for a low cross that Vincent Kompany hacked clear and then playing a central role in Argentina’s opener with a pirouette and pass to Di Maria.
Di Maria’s subsequent pass was intended for the overlapping Pablo Zabaleta, but it flicked off Jan Vertonghen’s right foot and into the path of Higuain, who lashed in his first goal of the tournament.
– Di Maria trudges off –
Messi then produced a cleverly weighted pass to Di Maria, who shifted the ball onto his left foot, only for Kompany to block.
Though seemingly anodyne, it was a moment that could have lasting repercussions for Argentina.
Di Maria injured himself while shooting and had to trudge off in the 33rd minute, with Benfica’s Enzo Perez coming on.
Belgium seemed slightly inhibited, but after Kevin De Bruyne saw a 25-yard shot boxed away by Argentina goalkeeper Sergio Romero, Kevin Mirallas headed narrowly wide from a Vertonghen cross.
Belgium coach Marc Wilmots pushed Marouane Fellaini further forward in the second half, but Argentina continued to threaten.
Higuain twice came close to claiming a second goal, first seeing a shot deflected wide by Daniel Van Buyten and then neatly nutmegging Kompany, only for his shot to clip the bar.
Wilmots reacted by introducing Romelu Lukaku and Dries Mertens, before hooking the ineffective Hazard.
Belgium began to apply pressure, with Fellaini heading a Vertonghen cross over the bar and De Bruyne having a shot deflected wide.
Messi should have made it 2-0 on the counter-attack in stoppage time, only for Thibaut Courtois to rush out and save, but Argentina held on nonetheless to join Germany and eternal rivals Brazil in the last four.