Salvador started the game in an attacking fashion and they could have gone ahead after only two minutes had been played, only for Irvin Herrera to see his close-range shot kept out at the bottom left corner.
The underdogs came close once more in the opening period when Andres Flores crossed for Pablo Punyed, who shot straight at Jamaica keeper Dwayne Miller in the middle of the goal.
Salvador continued to press for an opener following some early dominance and they almost found it on the stroke of half time, but for Richard Menjivar to be denied in the top corner by Miller.
Jamaica were much improved after the interval as they almost forced a lead through McCleary, who had two strong attempts kept out by Carrillo.
Salvador kept banging on the door in the second half, but their dominance failed to pay off when Punyed and Flores were wasteful from good positions.
Jamaica made them pay as they secured the game's vital goal in the 72nd minute when Jobi McAnuff had his shot parried, which allowed McCleary to steal in and prod home the rebound to secure victory.