Having opened the scoring with a 33rd minute header, Elliott caught goalkeeper Stuart Nelson off his line with a magnificent 30-yard lob to take his tally for the season to 14 league goals.
Hull had the better of the opening exchanges, as Nick Barmby sent a thumping half volley straight at Nelson from 20 yards. Moments later a free-kick from Stuart Green landed on top of the net.
Green then wasted a glorious opportunity when he latched on to Barmby's clever through ball only to be denied by Nelson. A low, right-footed drive from Jon Walters then whistled past the post as Hull continued to press.
The hosts eventually broke the deadlock, when Marc Joseph crossed from the right and Elliott rose superbly to head the ball over Nelson into the net.
Early in the second half, a sharp shot on the turn from Walters was well parried by Nelson.
However, Brentford were working really hard, and although they were creating no clear openings they had Hull penned back in their own half.
But the visitors were hit by a sucker punch nine minutes from time when Elliott picked the ball up 30 yards from goal and lifted an outrageous lob over Nelson and into the net off the underside of the cross bar.