The only goal arrived after just 12 minutes when Brady went down under Joey O'Brien's challenge.
The former Manchester United man picked up the ball himself and sent Jussi Jaaskelainen the wrong way to seal all three points for Steve Bruce's side.
Jake Livermore almost made the game safe in the second half when his shot beat Jaaskelainen but clattered the foot of the post.
West Ham had a penalty appeal for handball against Livermore waved away - but Allan McGregor was barely tested and he combined efforts of Modibo Maiga and Mladen Petric in attack saw the injured Andy Carroll's stock rise exponentially such was their toothlessness.
For Bruce's Hull the battle for top-flight survival is well ahead of schedule, with Tom Huddlestone impressing again in the centre of the park alongside strong showings from Livermore, Brady and Elmohamady.
West Ham were almost gifted an early opening when Rosenior's weak back pass needed swift attention from goalkeeper McGregor, as the visitors had the better of the early exchanges.
But then the moment on which the game turned. Elmohamady floated a cross from wide right in the direction of Brady, who was challenged unnecessarily by O'Brien.
After a moment's consideration referee Kevin Friend pointed to the spot and Brady gathered himself before sending Jaaskelainen the wrong way.
The Hammers were playing a more direct game than Hull, though Maiga did little to inspire confidence. His first sight of goal came after a strong run through the middle but he shot far too early to worry McGregor.
West Ham were close to levelling from a 23rd-minute corner though, Tomkins getting on the end of a Matt Jarvis corner only to see his header chested off the line by Elmohamady.
It was close enough for goal-line technology to be a real benefit and it showed only a fraction of the ball had crossed.
West Ham's breaks were becoming more frequent, Faye robbing Maiga at the last minute and Mohamed Diame producing an air-shot from 12 yards following Jarvis's pinpoint cut-back.
But Hull hit back and will have reached half-time amazed to be just one ahead. Sone Aluko's 34th-minute free-kick needed an athletic save, then a pair of Brady corners had West Ham begging for the whistle.
Curtis Davies met the first, with Maiga deflecting the effort up and on to the top of the crossbar. Brady then found Elmohamady with the follow-up and his header was well saved by Jaaskelainen at the near post.
The break did not obviously improve things for the visitors, with a linesman's flag the only thing denying Aluko just two minutes after the restart.
West Ham responded by attacking the home box with a handful of long balls, but Faye and Davies were coping well with the aerial examination.
Maiga's afternoon was cut short just before the hour mark when Sam Allardyce sent on Petric but Hull's own goal-shy striker, Danny Graham, remained in position.
He had a good chance to work the keeper in the 62nd minute when Brady's free-kick was touched towards him at the far post, but his off-balance shot was wayward.
The game was beginning to open up and when Graham held up the ball before teeing up the advancing Livermore a second goal seemed on.
The Spurs loanee took a touch before releasing a measured shot only to see it crash back off the base of the post.
Stewart Downing and Ricardo Vaz Te were given 20 minutes to change the game for West Ham, with Yannick Sagbo offered marginally less as Graham's replacement.
The Hammers were convinced they had a penalty in the 75th minute, with fervent appeals for a Livermore handball, but they went in vain.
West Ham went forward with plenty of urgency in the closing minutes but with no final product.