The Houston Dynamo lost defender Nathan Sturgis to a red card in the second half, but held on to see out the draw.
The home team took an early lead when Douglas Caetano headed home past Tyler Deric in the seventh minute.
Controversy abounded when Andre Hainault went unpunished after appearing to handle on the goal line in the second half.
Adam Moffat equalized for the American team, heading home Nathan Sturgis' delivery from close-in.
Sturgis saw red shortly after, going in late on an Olimpia player, but Houston held on despite the dismissal to secure the 1-1 draw and the vital away point.
The draw leaves the two teams tied atop their group, with two matches remaining. The winner will advance to the knockout round.
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