Hull came close early on, as a looping shot from Stephen Hunt forced keeper Chris Kirkland into a smart save, but only into the path of Nick Barmby, whose close-range shot seemingly hit the arm of defender Maynor Figueroa.
However, referee Mark Clattenburg was quick to waive away the appeals.
The home side had another chance on ten minutes, as Hunt found Barmby in the box with a pin-point crossfield ball, but the Hull skipper could only send the ball wide with a lunging first-time strike.
Geovanni then tried his luck for the Tigers, as his thunderous right-footed shot from 30 yards saw the ball fly just over the crossbar.
The visitors nearly broke the deadlock moments later, as Jason Scotland skipped passed the Hull defence to unleash low right-footed shot which flashed inches wide of Boaz Myhill's right-hand post.
Hesselink was next to come close for Hull, as Geovanni whipped in a cross onto the head of the Dutch frontman, but his glancing effort from eight yards whistled past the post.
Hull opened the scoring on the hour mark, as a Dean Marney corner was met by the head of Hesselink at the front post, who neatly nodded the ball beyond Kirkland and into the back of the net to register his first goal for Phil Brown's men.
Scotland had a chance for Wigan moments later, but the ex-Swansea man dragged his right-footed shot wide from 20 yards.
The Tigers were then 2-0 up on 68 minutes, as Kamil Zayatte found space down the right to play in a cross towards an unmarked Geovanni, who made no mistake from eight yards with a first-time right-footed effort, registering his third league goal of the campaign.
Wigan pulled one back on 87 minutes as substitute Jordi Gomez saw his shot saved, but only into the path of fellow sub Sinclair, who was able to head the ball past a scrambling Myhill and into the back of the net from close range.