The defeat ended any lingering hopes Bradford had of making a late push for the play-offs and cemented Hull's place in second spot.
It took the visitors just four minutes to open the scoring when Elliott, League One's top marksman, rammed home his 28th goal of the season. Craig Fagan caused panic in the home defence with a mazy run and slipped the ball to Elliott who fired home from ten yards out.
The Bantams had plenty of first-half possession but failed to test Boaz Myhill in the Hull goal.
At the start of the second half Colin Todd threw on winger Owen Morrison and Bradford immediately looked more dangerous.
Hull were penned back in their own half and Ben Muirhead should have levelled the scores but his side-footed effort flashed agonisingly wide.
Despite all their pressure Bradford couldn't force an equaliser and it was Hull that doubled their lead against the run of play in the 68th minute. Ryan France beat Lewis Emanuel on the right flank and pulled the ball back to Nicky Barmby who was left unmarked on the edge of the box. The former England man stroked the ball into the corner of Paul Henderson's goal to the delight of the large band of away supporters.
Hull's ninth away win of the season makes them favourites for automatic promotion while Bradford are left looking to build for next season.