The Hornets got off to a dream start barely 60 seconds into the contest when Tommy Smith found Grzegorz Rasiak in space and he in turn fed Will Hoskins, whose low cross was converted at the back post by Jobi McAnuff.
It continued an impressive return to form for the former Crystal Palace wideman who, having set up all four goals on Saturday, netted his first since Boxing Day 2007.
However, Brendan Rodgers' side were made to work hard thereafter as the visitors dominated possession but were unable to translate this into clear-cut opportunities.
The closest they came was when Martin Paterson forced a decent save out of Scott Loach, while Chris Eagles also sent a shot narrowly over.
But Watford always looked sharper going forward and underlined this with 12 minutes remaining when Tamas Priskin, who had only been on the pitch less than a minute, latched onto Jon Harley's through ball and emphatically beat Burnley keeper Brian Jensen.
And what was perhaps a flattering margin of victory was cemented in injury time when Priskin dispossessed an opponent on halfway and scooped into the opposition penalty area, choosing to ignore team mate Smith as he impressively curled his second of the game into the far corner.