La Albiceleste - who finished the contest without the injured Angel di Maria - will next face either Netherlands or Costa Rica, with tournament hosts Brazil up against Germany in the other last-four tie.
Argentina started proceedings brightly, as Higuain scored his first goal of the competition with a 'striker's finish' eight minutes in. Higuain volleyed in on the turn just inside the area after Di Maria's pass deflected off Jan Vertonghen and sat up kindly for the Napoli forward.
The South Americans, though, were rocked by Di Maria's forced withdrawal just past the half-hour mark, as he took a knock to his right knee and had to be replaced by Enzo Perez.
Belgium threatened twice before the break, as Kevin de Bruyne drilled a shot on target forcing a save from goalkeeper Sergio Romero before Everton forward Kevin Mirallas steered a diving header narrowly wide off a Vertonghen left-wing cross.
The second period was similarly lacking in goal-mouth action, although Higuain nearly doubled the lead in the 55th minute when he clipped the cross bar with a stinging strike after going on a surging run.
Soon after, Manchester United midfielder Marouane Fellaini powered a decent header just over at the other end off another accurate cross by Vertonghen.
Alejandro Sabella's men, however, were able to see out the latter stages in relative comfort, and could have grabbed a second goal in stoppage time but talisman Lionel Messi was foiled in a one-on-one situation by the impressive Thibaut Courtois.