Hudson homered in the first inning and the Diamondbacks coasted behind Haren (6-4), who scattered four hits with five strikeouts in seven innings.
The Nationals, who have lost five of seven games, had one extra base hit -- a double by Jesus Flores.
Washington starter Shawn Hill (0-2) lasted four innings, giving up all of Arizona's runs.
Handler slams Piers Morgan: 'You're a terrible interviewer'
Beautician charged with giving client fatal silicone butt injection