The Slovenia international lashed a right-footed shot into the bottom corner in the fourth minute of time added on to condemn Watford to a fourth successive league defeat.
Tigers defender James Chester headed past his own goalkeeper to gift Watford a 36th-minute lead in a first half bereft of goalscoring chances, but Hull striker Matty Fryatt pounced to turn home the first equaliser from close range six minutes into the second period.
Watford forward Chris Iwelumo restored the visitors' advantage when he headed home from six yards just five minutes later, but Hull responded again through Aaron Mclean's neat finish and Koren snatched all three points at the death with his fine 25-yard effort.
Hull made one enforced change to their starting line-up, with Tom Cairney back in for the injured Martin Pusic, while Marvin Sordell and Mark Yeates returned for Watford.
Hull winger Robbie Brady cut inside to unleash a shot from 20 yards just off target in the 10th minute, but neither side created a single chance until Watford striker Iwelumo headed Jonathan Hogg's ball in over the crossbar.
Watford's Troy Deeney went close with an angled drive and the visitors broke the deadlock with their third attempt on goal in the 36th minute.
Yeates got in behind a flat-footed Tigers' back four and his cross was headed past his own goalkeeper by Hull defender Chester from six yards.
There was time enough for Watford defender Lloyd Doyley to head straight at Hull goalkeeper Adriano Basso from inside the penalty area, but a largely forgettable first half ended with no further incident.
Hull were back on level terms six minutes into the second half when Fryatt converted Cairney's cross from six yards and Brady fired straight at visiting goalkeeper Scott Loach from outside the penalty area as the Tigers seized the ascendancy.
But Watford stirred themselves immediately. Sordell's angled shot from the corner of the penalty area was superbly turned away by Basso before Iwelumo headed Watford back in front.
Yeates again supplied the ammunition, his cross finding Sordell six yards from goal and the Hornets forward made no mistake with his close-range header in the 56th minute.
Hull refused to buckle though and after a spell of pressure equalised for a second time in the 70th minute.
Tigers defender Liam Rosenior burst forward down the right and his cross was lashed home by Mclean into the bottom corner from 12 yards.
Watford goalkeeper Loach was then at his alert best to tip away Cairney's cross-shot as the action flowed from end to end and the outstanding Yeates fired an angled shot against the post for the visitors after ghosting inside his marker on the edge of the area.
And with the clock ticking down deep in time added on Koren received a pass from Cairney 25 yards from goal and struck a fine shot into the bottom corner to snatch all three points for the Tigers.