Neither side were able to take control of the game in the first half but Sammy Ameobi threatened to light up a dull contest with a superb effort from 25 yards to force David Stockdale into a smart save.
Hull started to dominate possession following the break as Middlesbrough started to play from deep within their own half.
The hosts broke the deadlock in the 62nd minute through Brady, whose free kick proved too much for Steele to keep out.
Middlesbrough's confidence was clearly dented by Brady's strike and the midfielder went close again as he tested Steele with a low drive.
Hull were comfortable in the final stages and were able to cruise to a vital win that sees them take a big step towards promotion.