Haiti doubled the advantage 12 minutes later when Nicaraguan defender Manuel Rosas deflected the ball into his own net for an own goal on a scorching hot day in Frisco.
The Haitians are unbeaten in Group B. Second-placed Costa Rica face Bermuda later on Thursday.
Haiti and Costa Rica meet in New Jersey on Monday.
(Reporting by Rory Carroll; Editing by Greg Stutchbury)