The Argentina captain, 27, was kept at bay but Napoli striker Gonzalo Higuain fired home from inside the box.
While Messi’s side had already qualified for the last 16, even a win would not have been enough for Jamaica. Forward DeShorn Brown made a mark though, posing for a selfie with Messi on the pitch after the final whistle.
Defender Kemar Lawrence cleared the ball off the line and Argentina’s Higuain and Angel Di Maria both hit the bar as the 2014 World Cup runners-up easily outplayed a nation 62 places below them in the world rankings.
Earlier, Uruguay and Paraguay also went through from Group B after a 1-1 draw in which both sides scored through headers from corners. Atletico Madrid defender Jose Gimenez had given Uruguay the lead only for Paraguay striker Lucas Barrios to equalise just before half-time.
Paraguay qualify as runners-up and will play the winners of Group C, most likely Brazil, while Uruguay finished as one of two best-placed third teams and will face hosts Chile. Venezuela are currently third in Group C, the position Argentina will face, although all four teams in the pool are all on three points.