The visitors fell behind after half an hour when Victor Moses curled the ball in off the post, his first strike for the Latics since joining from Crystal Palace.
Hull looked to have turned the match around as youngsters Will Atkinson and Mark Cullen also opened their Premier League accounts, but Gohouri - another Wigan first-time scorer - struck with a late acrobatic effort to send the visitors down.
Due to a vastly inferior goal difference, Iain Dowie's team were already all but relegated before the start of play.
But they were cruelly denied what would have been a morale-boosting victory after Dowie's decision to field a youthful side - including Atkinson, Cullen and Tom Cairney from the start - almost paid off.
Wigan, who had secured survival last weekend, move up to 15th after rescuing their final home game of the season.
The hosts made a bright start, with Jordi Gomez sending a drive just wide of Matt Duke's left-hand post in the fourth minute and Hugo Rodallega having a close-range effort deflected behind shortly after. Gary Caldwell rose to meet the corner but could not connect properly.
At the other end, former Wigan midfielder Kevin Kilbane broke into the box but the danger was cleared by Gohouri. A minute later, goalkeeper Vladimir Stojkovic's poor kick fell straight to Cullen, who played a one-two with Atkinson before sending in a cross that Jan Vennegoor of Hesselink headed off-target.
Kilbane then picked out Atkinson in the box, who caught it first-time but saw his strike parried by Stojkovic, and the Irishman got a shot away himself in the 22nd minute which was wide of the mark.
Having soaked up some pressure, the Latics looked to hit back and Gomez deftly slipped Rodallega in on goal only for Steven Mouyokolo to make a vital interception.
The deadlock was broken on the half-hour thanks to a moment of quality from Moses, who collected Mohamed Diame's through-ball on the left, cut inside two defenders and lashed the ball across Duke and in off the far post.
Minutes later Moses had the chance to add another, but mis-cued his attempt from a knocked-down corner.
Hull had never been out of the match and three minutes before the break they found the equaliser they deserved, although in controversial circumstances.
Atkinson was the scorer, nodding Kilbane's cross past Stojkovic, but the goal appeared to have been ruled out for offside.
However, much to the consternation of Wigan's players, referee Phil Dowd chose to overrule his assistant, and Hull went in level at half-time.
The Tigers emerged for the second half looking lively and felt they deserved a penalty for handball when Maynor Figueroa blocked Cullen's shot.
But the endeavour of Gomez and Rodallega then led to a flurry of Wigan chances.
Gomez brought a save out of Duke with a shot from outside the area, and Rodallega tried to capitalise on some woeful Hull defending but fired wide.
The Colombian then made a better attempt, shooting just over after bringing down a ball on the run and he then teed up Gomez with a clever backheel that the Spaniard volleyed wide.
The Latics appeared to have all the momentum, but in the 64th minute Hull found themselves in front, with another young player getting his first senior goal.
This time it was teenager Cullen, who looked as if he could have been offside when he evaded his marker to head George Boateng's cross past Stojkovic.
Cullen tried his luck again with a drive 10 minutes from time but the effort went high and wide.
Moments later Wigan boss Roberto Martinez threw on Paul Scharner, who appeared to have the message "thanks" dyed into his hair.
And Scharner provided the assist for Gohouri in the dying moments as he fired an over-head kick past Duke.
Dowd and the stewards then had to deal with a pitch invasion before a final minute was played out and Hull's fate was sealed.