It ended a 528-minute drought for the forward and ensured La Albiceleste's three-match losing run at the quarter-final stage finally came to an end.
Argentina carved out the better openings but were dealt a blow just past the half hour when Di Maria limped off injured after seeing a goalbound shot blocked.
It left more focus on Messi but the diminutive forward stepped up to the task, fizzing a free kick inches over the bar on an afternoon when he equalled Diego Maradona's haul of 91 caps for his country.
Belgium did have opportunities as the match wore on with Kevin Mirallas planting a free header agonisingly wide while at the other end Higuain clipped the bar after a probing run and shot.
Marouane Fellaini then nodded over when well placed before an extraordinary finale saw Messi denied by Thibaut Courtois when clear on goal, with Axel Witsel blazing a rebound over just seconds later after Argentina had somehow scrambled Romelu Lukaku's cut-back clear of the six-yard box.
PRE-MATCH: Origi starts, three changes for Argentina: Liverpool target Divock Origi leads the line for Belgium with Chelsea's Romelu Lukaku on the bench. The Red Devils make one change from that extra-time success over the USA with Everton's Kevin Mirallas taking the spot of Dries Mertens. Meanwhile, there are three changes for Argentina. Man City defender Martin Demichelis is in for Federico Fernandez while Jose Basanta replaces the suspended Marcos Rojo at left back. Lucas Biglia also starts instead of Fernando Gago.
8' - GOAL! ARGENTINA 1-0 BELGIUM. Higuain breaks his goal drought with an instinctive volley from the edge of the area that Courtois doesn't even move for. The striker spun on a deflected pass from Di Maria and let fly after the first real mazy run from Messi.
33' - DI MARIA INJURY. The Real Madrid playmaker limps off after picking up a knock seeing a goalbound shot blocked. A real blow for Argentina. 40' - ARGENTINA CHANCE! Messi steps up and crashes a 20-yard free kick inches over the bar. Good effort!
42' - BELGIUM CHANCE! It should be 1-1 as Vertonghen whips a devilish cross in from the left for Mirallas who guides his free header wide from eight yards out.
52' - CLOSE! Higuain is tight to the left byline but is allowed to jink in and create a shooting opportunity with his effort taking a wicked deflection and spinning wide with Courtois going the other way.
55' - OFF THE BAR! A blistering counter attack sees Higuain weave past his marker and fizz a shot that clips the bar and bounces over.
61' - BELGIUM CHANCE! A left-wing cross is attacked by Fellaini who powers his header over the top. The Man United midfielder should have done better there.
90+4' - ARGENTINA CHANCE! Messi races clean through, it has to be 2-0... great save Courtois!!!
90+5' - BELGIUM ALMOST EQUALISE! Lukaku with a great turn and a vital interception denies his cut-back three yards out before Witsel fires the loose ball over the bar. Huge chance!
Argentina record their 22nd win in their 50th WC match against a European opponent.
Divock Origi (19 years 78 days) is the youngest player to start a World Cup quarter final since Pelé (17 years 239 days) on 19 June 1958.
Argentina are the fifth team against which Belgium lose two World Cup matches. They have never lost three against one team.
In years there were semi finals, Brazil and Argentina had never been in the last four in the same edition of a World Cup until this year.
Argentina have now won their first five matches of a WC for the first time. At the inaugural WC in 1930, they won the first four matches but lost the fifth match: 4-2 against Uruguay in the final
Lionel Messi pulled level with Diego Maradona on 91 caps for Argentina.
Gonzalo Higuaín ended his goalscoring drought of 528 minutes with Argentina.
It was Higuain's fifth World Cup goal in total.
Argentina and Germany are the only teams to have scored the opening goal in each of their five matches so far.
Belgium have failed to score a first-half goal in each of their last six World Cup matches.
Lionel Messi completed 100% of his passes (13) in the first half.
Argentina have hit the woodwork three times at this World Cup. Only France (5) and Greece (4) have hit it more often.
Argentina advance to their first World Cup semi-final since 1990, when they finished as tournament runners-up.
TALKING POINT: Will Messi now lead Argentina to the title? La Albiceleste produced arguably their best display so far and should probably have sewn up victory prior to Belgium's late spell of pressure. With Angel Di Maria limping off there could yet be more reliance upon Messi but the number 10 looks to be revelling in the expectation and who would bet against him stepping up to the plate once more, particularly with the Golden Boot still up for grabs?
MAN OF THE MATCH
Lionel Messi (Argentina): The Barcelona forward was irresistible at times in the first period and almost added to his tournament tally with a delicious free kick. In the second period he was the fulcrum for Argentina's counter attacks with the only blemish on his display a late one-on-one that saw Thibaut Courtois deny him.
ARGENTINA: Romero 6, Zabaleta 7, Demichelis 7, Garay 7, Basanta 6, Mascherano 7, Biglia 6, Di Maria 6, Lavezzi 6, Messi 8, Higuain 7. Subs: Perez 6, Palacio 6, Gago n/a.
BELGIUM: Courtois 7, Alderweireld 6, Van Buyten 6, Kompany 7, Vertonghen 7, Witsel 6, Fellaini 6, De Bruyne 6, Mirallas 5, Hazard 6, Origi 5. Subs: Mertens 6, Lukaku 6, Chadli 5.
THE MATCH IN A TWEET
- Sports & Recreation
- Lionel Messi
- Gonzalo Higuain
- Angel Di Maria
- Thibaut Courtois
- Kevin Mirallas