The affair looked to be petering out into a terrible 0-0 snore draw, but Koren's fine 77th minute strike into the bottom corner ensured the Tigers recorded back-to-back wins for the first time this season.
Substitute Nobby Solano picked out the Slovenian star with a raking pass before the midfielder rattled in his fourth of the campaign from 25-yards.
Earlier Jason Scotland nearly put Ipswich ahead but Roy Keane remains under pressure after a poor display saw the Tractor Boys suffer a third straight defeat.
Keane bore the brunt of criticism following his team's defeat at Barnsley last week and he will come under fresh scrutiny from fans in the next seven days.
The manager opted to drop goalkeeper Marton Fulop following that humbling, Brian Murphy coming in, while former Hull man Damien Delaney started.
The Tigers went into the clash on the back of a win at Preston but after five home games without victory, they were languishing in dangerous territory.
Hull chief Nigel Pearson was forced to re-jig his line-up after losing centre-back Daniel Ayala to a hamstring injury.
Kamil Zayatte dropped into defence, with John Bostock - back from suspension - slotted into midfield.
Zayatte showed early signs of nervousness as he allowed Scotland room to shoot at Vito Mannone but the keeper saved with his feet.
Hull's jitters set the tone for the opening exchanges as Ipswich also struggled to stamp their authority on the match.
Koren first tried to illuminate a dull Hull skyline
however he could only warm the hands of Murphy.
Confusion reigned once again on the half-hour as Zayatte got in a muddle with Mannone from a cross, but thankfully for the defender the on-loan Arsenal man bravely punched clear.
Incredibly Hull nearly took the lead when Kevin Kilbane, who endured a difficult afternoon, saw his header bounce off the woodwork twice just before the interval.
And 30-seconds later skipper Ian Ashbee rattled a shot off the up-right as the Tractor Boys went into the break unscathed.
The turgid pattern of play continued into the second period and both manager's made changes just before the hour in an attempt to eke out a goal.
A double swop from Pearson saw the introduction of Mark Cullen and Nick Barmby in place of Kilbane and Bostock, while Tamas Priskin come on after Scotland failed to capitalise on the solitary opening of the first 45 minutes.
Carlos Edwards let fly from 25-yards but his strike was tantamount to the lack of quality on show until Koren seized control of the game for his team to apply the match-winning finish.