The Napoli striker struck a superb goal in the first half and that was enough to see off a disappointing Red Devils side
Much has been made of Argentina's reliance on mercurial captain Lionel Messi during the tournament in Brazil, but they proved they are no one-man team with an impressive display in Brasilia on Saturday.
Messi once again led by example as he equalled Diego Maradona's tally of 91 caps for his country, but it was Higuain who proved to be Argentina's match-winner with a fine early strike.
The Real Madrid striker also hit the crossbar in the second half as the South American nation produced arguably their best performance of the competition to secure a last-four spot against either the Netherlands or Costa Rica.
Argentina beat Belgium in the semi-finals in 1986 in the last meeting between the two sides, then went on to be crowned world champions, and on this evidence they are capable of repeating that feat for the first time since those finals in Mexico.
The Albiceleste came in for criticism following their disjointed display against Switzerland in the last 16, but started on the front foot and were rewarded when Higuain put them in front with a fine finish on eight minutes.
Unsurprisingly, Messi was involved, carrying the ball forward from the middle of the park and picking out Angel Di Maria, whose pass deflected invitingly for Higuain to swivel and dispatch a fierce effort into the far corner of the net.
Di Maria was then thwarted by a Kompany block after Messi had picked him out with a sublime pass and the Real Madrid winger injured himself in the process, with Enzo Perez introduced in his place.
Messi was at the heart of everything and blasted a free-kick just over the crossbar after being upended on the edge of the penalty area 39 minutes in.
Argentina were brimming with confidence, but they were almost caught out four minutes before the break, when Mirallas' powerful header flew narrowly wide after he was picked out by an inviting Jan Vertonghen cross.
Higuain was a real handful for the Belgium defence and almost doubled his side's lead with a stunning solo goal nine minutes into the second half.
The striker embarked on a bursting run, in which he skipped past Kompany all too easily before unleashing a venomous right-footed shot that struck the top of the crossbar.
Chances were few and far between up the other end, but Marouane Fellaini should have tested Sergio Romero when he headed off target after Vertonghen whipped in another dangerous cross.
Belgium threw men forward in an attempt to force extra time and saw a late deflected Kevin de Bruyne shot flash just wide.
Messi then spurned a chance to finish Belgium off three minutes into time added on when he raced clear, but Thibaut Courtois stood tall to thwart him.
Axel Witsel sliced a late volley over the bar from the edge of the box, leaving Argentina to hold on to seal their place in the semi-finals, where they will face the winner of the quarter-final between Netherlands and Costa Rica.