The Napoli striker struck a superb goal in the first half and that was enough to see off a disappointing Red Devils side.
Gonzalo Higuain scored his first goal of the FIFA World Cup as Argentina beat Belgium 1-0 at Estadio Nacional to reach the semifinals.
Much has been made of Argentina's reliance on mercurial captain Lionel Messi during the tournament in Brazil, but Alejandro Sabella's side proved it is no one-man team with an impressive display in Brasilia on Saturday.
Messi once again led by example as he equaled 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 its best performance of the competition to secure a last-four spot against either the Netherlands or Costa Rica.
Argentina beat Belgium in the semifinals in 1986 in the last meeting between the two sides, then went on to be crowned world champion, and on this evidence the team is capable of repeating that feat for the first time since those finals in Mexico.
Belgium had been billed as a dark horse to go all the way, but the team was not at the races in the capital as it bowed out with a whimper.
Jose Basanta replaced suspended fullback Marcos Rojo in the Argentina starting lineup, while Martin Demichelis and Lucas Biglia also came in.
Belgium coach Marc Wilmots handed a start to Kevin Mirallas at the expense of winger Dries Mertens.
Argentina came in for criticism following a disjointed display against Switzerland in the last 16, but started on the front foot and was rewarded when Higuain put his side in front with a fine finish just eight minutes in.PHOTOS: U.S. fan reactions | Beautiful people in Brazil
Not surprisingly Messi was involved, carrying the ball forward from the middle of the park after Vincent Kompany had lost possession then picking out Angel di Maria, whose pass deflected invitingly for Higuain to swivel before firing into the far corner of the net with a clinical right-footed strike.
Di Maria was 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, so was replaced by Enzo Perez.
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 after 39 minutes.
Argentina was brimming with confidence, but was almost caught out four minutes before the break, when Mirallas' powerful header was off target after he was picked out by an inviting Jan Vertonghen cross.
Higuain was a real handful for the Belgium defense and almost doubled Argentina's lead with a stunning solo goal nine minutes into the second half.
The striker embarked on an incisive run, in which he skipped past Kompany all too easily before unleashing a venomous right-footed shot that struck the top of the crossbar.
Marouane Fellaini should have tested Sergio Romero, but 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.
Belgium should have made Messi pay when Romelu Lukaku and Axel Witsel came close to producing a dramatic equalizer, but Argentina held on to progress.