Paraguay’s earlier 1-1 draw with Uruguay meant La Albiceleste had already advanced to the knockout stages of the competition before their final Group B game, but they were keen to put on a performance on captain Lionel Messi’s 100th appearance for his country.
However, despite creating a number of chances, especially in the opening 45 minutes, Argentina had to rely on a solitary Gonzalo Higuain strike after 10 minutes to secure all three points.
Manchester United’s Angel Di Maria turned in a man of the match performance, and his early mazy run almost led to Higuain finding the opener but his effort was deflected over the bar.
The Napoli striker wasn’t to be denied for long, however. He picked up Di Maria’s pass in the middle of the box, was allowed the time and space to turn, and coolly slotted the ball past Dwayne Miller in the Jamaica goal.
He nearly got his second soon after when he was left all alone by the Jamaica defence and lifted his effort over the onrushing Miller but could only watch as his lob bounced off the top of the bar.
Messi was desperate to score on his landmark evening and came close following a lovely layoff from the goalscorer Higuain.
The Argentina captain shifted the ball beautifully on to his left foot before curling his effort just wide of the post.
Higuain went close again before Di Maria ran the length of the pitch and chipped an effort over Miller, only to see the ball cleared off the line.
The United winger then forced a good save from Miller on the stroke of half time after blasting an effort from the edge of the box but Argentina somehow managed to go into the break only leading 1-0.
They started the second half in similar fashion, however, controlling possession and peppering the Jamaica goal with efforts.
Di Maria came closest to extending his side’s lead when he cut inside and crashed a curling left foot effort off the bar from the edge of the box.
Messi then went close twice in quick succession, being denied by Miller on both occasions. The Barcelona forward saw his free kick from 25 yards saved before his attempted chip just wasn’t high enough to beat the shot-stopper after confusion in the Jamaican defence.
Argentina failed to carve out many more clear chances of note, despite enjoying more of the ball.
Lance Laing fired a chance well over the bar from a free kick for Jamaica, before Deshorn Brown got his side’s first attempt on target when he shot straight at Sergio Romero from distance.
Earlier, Paraguay and Uruguay both secured passage to the quarter finals from Group B following a 1-1 draw.
Jose Gimenez’s strike on the half hour mark for the holders was cancelled out by Lucas Barrio just before half time.
A point meant Uruguay qualified as one of the best placed third teams.