The Tigers made it three successive wins on the road, and their sixth victory in their last nine league matches, with a goal just before half-time from on-loan Sunderland midfielder Meyler and winger Brady's thumping free-kick midway through the second half.
Gianfranco Zola's Watford, unbeaten in their previous seven having won five of them, had to settle for Troy Deeney's stoppage-time consolation, while second-half substitute Almen Abdi hit the post for the hosts shortly after replacing Daniel Pudil, but it was not to be their day.
Save for an early shot from Hull striker Jay Simpson and Watford defender Nathaniel Chalobah's blocked 20-yard shot in the 17th minute, neither side mustered a single effort on goal during the opening half-hour.
Hull midfielder Robert Koren let fly with a strike from similar distance that was comfortably held by Manuel Almunia, but the biggest cheer, from the away end at least, came when Tigers defender Jack Hobbs replaced the injured Paul McShane in the 27th minute.
Hobbs made his first appearance for the club since March after undergoing cruciate knee ligament surgery towards the end of last season.
Hull had slowly began to build up a head of steam towards the end of the first period and were rewarded with the game's opening goal in the 41st minute.
Corry Evans smashed a blistering shot from the edge of the penalty area against the crossbar and midfield colleague Meyler reacted quickest to head home the rebound.
Deeney pulled his shot from outside the area off target shortly after the restart and Hull goalkeeper David Stockdale rescued the visitors with a brilliant save to keep out Mark Yeates' free-kick soon after as the home side attempted to step up a gear.
But Hull twice threatened to extend their lead through long-range strikes from Koren and Brady as Watford struggled to make headway.
Hornets substitute Abdi, a 65th-minute replacement for Pudil, struck the woodwork with a superb shot from inside the area shortly after coming on.
Watford were then made to pay. Defender Fitz Hall fouled Meyler in a central position 25 yards from goal and Brady thumped home an unstoppable free-kick, high into the net for the decisive second goal in the 73rd minute.
Deeney did pull one back for the Hornets in the 92nd minute when converting Abdi's cross, but Hull held on for victory.