Netherlands international Vennegoor of Hesselink has been linked with moves back to his homeland.
The incident happened shortly after half-time when Dunne and Vennegoor of Hesselink challenged for a corner.
Paul Hartley, Jan Vennegoor of Hesselink and Shunsuke Nakamura all left the club in the summer.
Vennegoor of Hesselink then slotted home at the death after Thomas Sorensen failed to hold Jimmy Bullard's shot.
Meanwhile, Jan Vennegoor of Hesselink has been an able replacement for John Hartson.
BBC: SPORT | Football | My Club | Celtic | Celtic's title relief
Jan Vennegoor of Hesselink fired Celtic into a first-minute lead with a shot from the edge of the box.
The Latics were on top after the break but Vennegoor of Hesselink met Dean Marney's corner to head Hull in front.
Celtic went ahead when Vennegoor of Hesselink rose highest in a congested penalty box to glance in a corner from Nakamura.
Hull's equaliser came from the penalty spot after Sol Campbell was adjudged to have brought down a seemingly offside Jan Vennegoor of Hesselink.
The home side had a deflected Tom Cairney shot and a header wide by Jan Vennegoor of Hesselink to show for their efforts.
Vennegoor of Hesselink is out, as is leading goalscorer Samaras, and Scott McDonald, the club's top scorer last term, has yet to rediscover his Midas touch.
The home team did fashion a few late chances, with Vennegoor of Hesselink heading over and David Weir making a vital block to deny Derek Riordan.
Jan Vennegoor of Hesselink bundled in the second goal, Aiden McGeady powered home the third from 25 yards and the fourth was volleyed in by Darren O'Dea.
High crosses continued to cause problems for both sides and Vennegoor of Hesselink flashed a header wide before Steven Pressley's powerful nod was kept out by Combe.
Vennegoor of Hesselink beat the offside trap in the 17th minute only to drag his shot wide and the Dutchman then headed wide from Lee Naylor's corner.
Jan Vennegoor of Hesselink struck the winner in the dying minutes against 10-man Stoke at the weekend to haul themselves out of the Barclays Premier League relegation zone.
Hull responded by pouring forward again and went close to breaking the deadlock when Geovanni curled in a cross that Vennegoor of Hesselink stooped to head inches wide.
The Gunners took the lead through Andrey Arshavin after 14 minutes but Jimmy Bullard leveled with a penalty after 28 minutes when Sol Campbell fouled Jan Vennegoor of Hesselink.
The Potters would have moved up to seventh in the Premier League with victory at the KC Stadium, but were denied a point by a late strike from Jan Vennegoor of Hesselink.
That all changed on the hour mark when Vennegoor of Hesselink met Marney's corner with a fierce downward header for his first goal since joining the club at the start of September.
The German right-back's low cross was volleyed first time by Vennegoor of Hesselink and goalkeeper Janos Balogh was slow to get down to his left as the ball trickled into the net.
Sorensen dived to block but failed to divert the ball out of harm's way and it fell straight into the path of Vennegoor of Hesselink, who made no mistake with a straightforward finish.
Both players needed treatment but while the Villa defender was able to play on following stitches to a head wound, Vennegoor of Hesselink was attended to for seven minutes before being stretchered off.
City also went close to going ahead moments after the break when a curling cross from the excellent Bernard Mendy only just eluded Vennegoor of Hesselink and an onrushing Cullen at the back post.
The Celtic striker limped off soon after, being replaced with Vennegoor of Hesselink, who had remained on the bench despite having broken his six-month barren scoring spell after coming on as a substitute against Hamilton.
Chelsea pair Arjen Robben and Khalid Boulahrouz, Celtic duo Evander Sno and Jan Vennegoor of Hesselink, Wigan's Danny Landzaat, Robin van Persie of Arsenal, Liverpool striker Dirk Kuyt and Blackburn defender Andre Ooijer have all received call-ups.
BBC: SPORT | Football | Internationals | Van Persie out of Holland squad
Jan Vennegoor of Hesselink battled with a posse of Killie defenders at the edge of the penalty box and when the ball broke to Maloney, he curled it first time into the top corner of the net.
The points were virtually secured when Mallo failed to gather Nakamura's low cross at the front post and Vennegoor of Hesselink beat substitute defender Dean Holden to the ball to bundle it over the line from four yards.
And, although the early goal visibly rocked Celtic's confidence, the home side began to take control of midfield and Scott McDonald fired just over from 20 yards, while a head flick from Jan Vennegoor of Hesselink drifted just wide.
Aquilani placed a shot just wide after an overhead ball from Ryan Babel was only half-cleared but Hull did create a chance of their own when Jan Vennegoor of Hesselink bulldozed through the Liverpool defence before heading straight at Pepe Reina.
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