STORY: Messi, competing in his fifth World Cup at age 35, has won every other major title in his career but has failed to lift the coveted trophy despite making the final in 2014.
But his 64th minute strike that was followed by substitute Enzo Fernandez's sublime effort three minutes from time, reignited their hopes of advancing past the group stage after their shock 2-1 loss to Saudi Arabia in their opener.
Messi, who equalled Diego Maradona's Argentina record of 21 matches and eight goals at the World Cup, was nowhere to be seen for more than an hour before picking up an Angel Di Maria pass, finding just enough space and rifling in from 20 meters.
Substitute Fernandez made sure of the victory when he curled a superb shot into the top corner.
Argentina, on three points, can guarantee progress with a win over Poland, top on four, in their final game on Wednesday.