Goals from Ricardo Alvarez and skipper Lionel Messi ensured a winning send-off for the home side at La Plata, north of Buenos Aires, before they head to Brazil.
But the Argentinian squad will have raised eyebrows in Britain showing off their politically-charged banner declaring "Las Malvinas Son Argentinas (The Malvinas are Argentine)" to the 52,000 crowd before kick off.
The banner is regularly put on show before Argentina's games. But the proximity to the World Cup brought new attention.
Tensions have resurfaced in recent years with Argentina infuriated by the Falkland's government's search for oil in surrounding seas.
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Diplomatic tensions over the Falklands have added a confrontational edge to a series of titantic battles between England and Argentina at the World Cup.
Four years after the World Cup in 1986, Diego Maradona outraged the English with his punched "Hand of God" goal in the 2-1 quarter-final victory in Mexico.
Maradona later said bitterness over the Falklands conflict had motivated the Argentines against England.
In 1998, an epic last-16 match at the World Cup in France ended in a 2-2 draw with Argentina prevailing in a penalty shoot-out.
The match was famous for the red card shown to England's David Beckham for kicking Diego Simeone.
Four years later Beckham avenged the loss at the 2002 finals in Japan, scoring the only goal in a 1-0 victory over Argentina which helped to eliminate the South Americans in the first round.