The Fulham forward struck in the 36th minute at the Sun Life Stadium in Miami Gardens while goalkeeper Tim Howard made some key saves as the visitors played a full part.
Honduras almost went ahead when Jerry Bengston got ahead of the defence and broke into the box, firing a shot Howard saved at point-blank range and the Everton keeper then kept out Carlo Costly's effort.
On target: Clint Dempsey (right) struck for the USA
New man: Jurgen Klinsmann
The hosts took the lead when Steve Cherundolo slipped a short pass to Brek Shea who in turn sent a firm, low cross into the area which was dummied by Jozy Altidore and deflected off the heel of Michael Orozco Fiscal as it went through his legs.
The ball reached Dempsey who dragged the ball back to his left foot and bent a curling left-footed shot from 15 yards which went into the left-hand corner of the goal past keeper Donis Escobar.
Honduras continued to attack, Boniek Garcia, Roger Espinoza and Bengston all producing efforts on goal.
Dempsey did have the ball in the net again six minutes from time but his header was disallowed for a foul on Maynor Figueroa.
The victory was the first for Klinsmann in four games since he replaced Bob Bradley in July.
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