Bees boss Martin Allen rested several of his first-team players with the play-offs just around the corner and they got off to the worst possible start when in the first minute, Nick Barmby's corner found the unmarked Leon Cort who headed in off the underside of the bar.
Hull were passing the ball around well and it wasn't until the half-hour mark that Brentford had their first chance when Chris Hargreaves' goalbound header was blocked by Damien Delaney.
However, they went in level at the break when Jerrome Sobers - making his league debut - headed in Tabb's corner.
The second half failed to find any real rhythm with few chances created.
Those that were fell the way of Hull and Stuart Elliott in particular. First he spurned a glorious chance when he somehow side-footed the ball back across the face of the goal from Scott Wiseman's cross before firing over from a tight angle after being found well inside the box.
That was as good as it got until the 86th minute when a long ball upfield bounced in favour of Tabb.
But there was nothing fortuitous after that as he expertly cut inside the last defender before curling his shot past Boaz Myhill into the top corner.