Dempsey's goals in the 25th and 64th minutes were created from crosses from
The U.S. is 13-0 in Gold Cup openers.
Dempsey has 43 international goals, 14 behind
Carlos Discua scored his first international goal, in the 69th minute, for Honduras.
"It wasn't our best performance, but we're happy to get three points from our first game," Dempsey said.
The first goal developed when DeAndre Yedlin played a short corner kick to Bradley, who crossed on a bounce to the far post.
Henry Figueroa's clearance try back to Bradley's side was picked up at the side of the six-yard box by
Goalkeeper Donis Escobar kicked the ball out with his right foot and it popped up to Dempsey, who nodded it in from six yards.
Bradley's free kick from the flank led to the second goal. Escobar stayed on his line and an unmarked Dempsey jumped four yards out and headed inside the far post.
Bradley became the 16th U.S. male to make 100 international appearances. At 27 years 341 days, he is the fourth-youngest after Donovan (26-96), Cobi Jones (27-239) and Marcelo Balboa (27-320).
Haiti draws with Panama, 1-1
Duckens Nazon scored on a nifty breakaway move in the 85th minute to give Haiti a 1-1 tie with Panama in the CONCACAF Gold Cup opener Tuesday night.
Nazon took a long pass down the right side and beat defender Harold Cummings with a move to the inside before shooting to the far post, past goalkeeper Jaime Peneda.