The Tigers beat Swansea 2-0 on August 7 and emulated that scoreline against Derby tonight in a game which also saw midfield ace Jimmy Bullard make his first appearance this season.
Ayala bundled home a scrappy opener from Tom Cairney's cross and Koren grabbed the second after Jay Simpson's effort was saved.
Bullard, who had not played since April as the club sought to shift his hefty wage from their precarious balance sheet, was given a warm welcome by fans who had at times turned on him at the tail end of last season.
And his cross led indirectly to the first chance of the game, Cairney lashing narrowly over after his midfield colleague's cross was cleared.
Shaun Barker headed Tomasz Cywka's corner wide at the other end and Paul Green and James Bailey were off target from long range before Alberto Bueno had a penalty appeal turned down.
Ayala failed to connect cleanly with Bullard's corner, the ball flashing wide of the Spaniard's shoulder.
But the on-loan Liverpool youngster was more assured in his regular defensive role, denying Bueno a sight of goal.
Rams keeper Steve Bywater denied Simpson before the hosts broke the deadlock two minutes from half-time.
Simpson and Ayala both went for Cairney's cross after good work by Craig Fagan, and it was the defender who appeared to get the final touch to send the Tigers in a goal to the good.
Derby boss Nigel Clough threw on Kris Commons early in the second half and the winger soon threatened, shooting just over from 20 yards.
Hull's other on-loan defender, Anthony Gerrard, suffered an injury when making a bold block following a Rams corner, but the Cardiff man soon returned to the action.
The lively Commons should have levelled from Ben Pringle's cross but skewed his effort wide.
Bywater denied Simpson at the other end before Hull finally made the game safe.
Andy Dawson and Simpson combined and, when the latter's cross-shot came back off Bywater, Koren turned and finished from 10 yards.
Home keeper Matt Duke saved well from Commons and Bullard went close in stoppage time, but there was no further addition to the score.