M'Baye Niang scored one goal and made another on his Watford home debut as 10-man Burnley's miserable away record continued.
Sean Dyche's side, who have not won on their travels in any competition since last May, lost midfielder Jeff Hendrick to a sixth-minute red card for a two-footed challenge on Jose Holebas.
Niang, signed on loan from AC Milan last month, then crossed for Troy Deeney to head his third goal in four matches.
The winger then guided in Holebas' left-wing cross with a fine header just before half-time.
Ashley Barnes gave Burnley hope by scoring a penalty with 12 minutes left after Sebastian Prodl handled Joey Barton's shot - but they could not equalise.