Koren’s cross was turned in by Millwall’s Jack Smith early in the second half and his late volley secured Hull’s fourth win on the bounce.
The win was also the Tigers’ first against the Lions in nine attempts, putting to an end a barren run that stretched back to April 1987.
Hull were unchanged from their 1-0 win at Coventry while Millwall made four changes from their 0-0 draw against Cardiff, with forward Jay Simpson ineligible against his parent club.
Against the formbook, the Lions started by playing with more composure than the Tigers as Millwall edged the opening stages.
But it was Hull who created the first opening after 15 minutes as Liam Rosenior’s
perfectly-weighted pass put Matty Fryatt through on goal, but the striker was denied by the legs of Steve Mildenhall in the Millwall goal.
Both teams, whilst comfortable in possession, were lacking real quality in the final third in what was otherwise an open first half.
Aaron Mclean could only drag a snap-shot wide for Hull while Fryatt had the ball in the back of the net when put through but the striker had already been ruled marginally offside.
Millwall could have taken a lead into the interval through a Brian Howard free-kick, but his curling effort from the edge of the box was tipped around the post by Hull keeper Peter Gulacsi.
Hull started the brighter of the two teams after the break with Mclean hitting a powerful strike straight at Mildenhall.
But the keeper was soon at fault for Hull’s opener, getting in a mix-up with centre-back Shane Lowry which allowed Koren to engineer some space down the left. The Slovenian then fired across goal and Smith could only turn into his own net.
The Tigers looked to press home their advantage and poured forward, James Chester wasting Andy Dawson’s pinpoint cross by heading over when unmarked in the box.
Millwall then came close to an equaliser when James Henry’s deep cross found Darius Henderson, but the striker’s header was well blocked by Gulacsi.
The second half was providing much more entertainment for the fans at the KC Stadium, with Henderson again going close with a rasping drive that flew just over.
As the game entered the final stages Hull had shouts for a penalty turned down as Fryatt went down under pressure from Lowry but referee David Coote ignored the protests.
Millwall sniffed a point and came inches away from grabbing the equaliser as Paul Robinson almost capitalised on poor positioning by Gulacsi, but his header came agonisingly back off the bar.
Yet despite the Millwall pressure, Hull put the game to bed with 10 minutes left. Fryatt nodded down a long ball from Gulacsi and Koren volleyed home his seventh goal of the season from the edge of the box, low into the bottom corner of the net.
Fryatt almost set up a third but substitute Richard Garcia was well closed down by Mildenhall, but Hull went on to close out the final minutes with relative ease.