The visitors went into the contest on a six-match unbeaten streak, and after a quiet opening to the game it was they who were the first to come close when Josh Clarke fired narrowly over Eldin Jakupovic's goal.
Hull's own threat was minimal in the early stages of the game, with curling efforts from Diame and Andrew Robertson the closest they came to breaking the deadlock in the opening half-hour.
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However, they were handed a breakthrough in fortuitous circumstances shortly after the half-hour mark when Robertson latched on to Harry Maguire's pass over the top and saw his subsequent cross turned into his own net by Dean.
Diomande would have an even better chance to double the advantage just a minute later when Alex Bruce was fouled inside the area to give the home side a free kick, but once again Button denied the striker from the resulting penalty.
Button was beaten with six minutes remaining of the half as Robertson burst into the box before unleashing a powerful strike towards goal, but this time the woodwork came to the visitors' rescue as his effort came back off the crossbar.
The second goal finally arrived right on the stroke of half time, though, when Diame bundled the ball home from close range after seeing his initial effort saved by Button.
Brentford made a brighter start to the second half and created a rare good chance in the opening minutes after the interval when Marco Djuricin turned inside the box, only to fire his subsequent effort straight at Jakupovic.
Button continued to be the busier of the two keepers, though, and after watching a Maguire header fly wide he then got down well to deny Sam Clucas shortly after the hour mark.
Brentford came close themselves when Sam Saunders fired a free kick narrowly wide late on, but the Bees failed to come up with a response as they missed the chance to move up to ninth in the table.