Haiti were the first team to threaten as they won a free kick just outside the box and Mechack Jermone curled an effort towards goal, but his strike hit the top of the crossbar and bounced over.
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The States hit back with a good opportunity of their own as Aron Johannsson weaved his way past two defenders before teeing up Michael Bradley on the edge of the area, but he sent his shot wide of the post.
Gyasi Zardes replaced Jozy Altidore at the break and made an immediate impact to set up Dempsey for his side's goal. The forward raided down the left and cut the ball back for his teammate in the six-yard box, and the Seattle Sounders man guided the ball into the net.
Haiti continued to put the USA under pressure as Kim Jaggy found space to carve out a cross down the left, but Guerrier could only head his effort past the post.
Collat's side upped the ante late in the match as they pushed for an equaliser and Jeff Louis forced Guzan into a low save, but the USA held out for the win to secure their place in the last eight of the competition.