Koren, a second-half replacement for Jay Simpson, headed home Robbie Brady's cross in the 83rd minute after Ipswich substitute Anthony Wordsworth had cancelled out Brady's first-half penalty.
Victory for the Tigers lifts them six points clear of nearest challengers Watford, who slipped to a surprise defeat at Peterborough, with four games left to play.
The visitors dominated the early exchanges. James Chester lashed an early shot over the crossbar following a corner and Simpson's goalbound effort was blocked by Ipswich defender Aaron Cresswell.
Hull took a 28th-minute lead through Brady's penalty. Referee Oliver Langford pointed to the spot following Guirane N'Daw's challenge on Meyler and Brady coolly side-footed the ball, left-footed, into the bottom corner.
Ipswich regrouped during the interval and after gaining an immediate foothold after the restart the home side struck a 55th-minute equaliser with their first attack on goal.
Defender Luke Chambers broke forward down the right and his cross was met by substitute Wordsworth, who steered his header into the bottom corner from six yards.
Home striker Daryl Murphy then headed Wordsworth's free-kick over the crossbar, while Carlos Edwards headed wide as Ipswich's confidence soared.
Hull responded through Brady's shot from outside the area that flew wide, but the visitors were dealt a blow when midfielder Corry Evans went off injured, with Ahmed Fathi stepping off the substitutes' bench.
Visiting goalkeeper David Stockdale saved brilliantly to keep out Murphy's thumping shot from inside the area and just as it appeared Ipswich had done enough to earn a point, Koren ghosted in to head home Brady's cross with seven minutes left.
Hull striker Matty Fryatt made his first league appearance of the season in the closing stages following an Achilles injury as the visitors held on to their lead.