Callum McManaman - who also made his appearance coming off the bench - equalised for the hosts with three minutes of normal time, after Kieffer Moore had given the Latics the lead in the first half with a thumping header.
Moncur, who hadn't featured since the Carabao Cup defeat to Leicester in September, was to have the final say though as his close range finish in the dying seconds saw the Town snatch all three points when staring defeat in the face just minutes earlier.
Luke Berry came into the starting XI for his first Championship start in place of the injured Izzy Brown, with Graeme Jones opting to keep the same team from the defeat to Brentford – except for the Chelsea loanee.
The Hatters had two great opportunities in the opening eight minutes with Harry Cornick – making his 100th appearance for the club – at the heart of both moves. Firstly, playing in Andrew Shinnie who skied an effort from close range, before Ryan Tunnicliffe’s goal-bound effort was cleared off the line by Dujon Sterling, having been picked out by the forward.
After a period of control from the Town, Wigan mustered their first real chance of the game as Chey Dunkley’s header from Lewis Macleod’s cross flew just wide of the bottom left corner.
Matty Pearson went close to grabbing his first goal since nodding in the winner at Blackburn Rovers, as he got on the end of Luke Berry’s free-kick, but sent it over when he really should have hit the target from six yards out with 26 minutes gone.
Kieffer Moore was to put the visitors in the lead after 35 minutes though, as he rose highest to nod into the top left corner in expert fashion from Sterling’s cross against the run of play.
The striker had the opportunity to double the lead and his tally when he again got on the end of Sterling’s low cross, but this time bent his effort narrowly wide of the bottom right corner.
Town had a great opportunity to equalise just six minutes after the restart when Berry brought down goalkeeper Jamie Jones’ poor clearance 25 yards from goal, he shaped to shoot but instead played it to Collins, but the striker fired right at the visiting stopper, who palmed it behind for a corner.
Three minutes later and Tunnicliffe should have opened his goalscoring account for Luton as Cornick picked the midfielder out on the edge of the box, he bent it towards goal, but again it was straight at Jones who was able to make the save.
Substitute Callum McManaman nearly made the perfect impact just two minutes after he came on as he burst through the Wigan midfield, cut it onto his left and bent an effort from 20 yards just wide of the bottom left corner – but the 28-year-old would certainly leave his mark on the game with three minutes to go.
Having completely miss-hit his initial effort, McManaman made no mistake with his second, rolling the ball into the bottom right corner.
Moncur had been brought on with an hour gone and had seen two free-kicks fly straight into the wall, but grabbed the all important winner, as Tunnicliffe’s expert cross fell kindly for the ex-Barnsley man, and he fired into the bottom left corner which sent Kenilworth Road into absolute pandemonium.
The result lifts the Hatters up to 20th in the table, with 20 points, moving them four points clear of the bottom three.
Town are next in action on Tuesday evening, as they take on Stoke City at the Bet365 Stadium.
Town: Shea, Bree, Pearson, Bradley, Potts (Bolton 20), Tunnicliffe, Mpanzu, Shinnie (Moncur 60), Berry (McManaman 71), Cornick, Collins.
Unused subs: Sluga, LuaLua, Jones, Butterfield.
Yellow: Moncur
Goals: McManaman 87, Moncur 90+3
Wigan: Jones, Robinson, Macleod, Morsy, Pilkington (Massey), Lowe, Garner (Gelhardt 64), Sterling, Mulgrew (Kipre), Moore, Dunkley.
Unused subs: Evans, Windass, Massey, Roberts, Kipre, Gyollai, Gelhardt.
Yellow: Dunkley, Pilkington, Garner
Red: Dunkley
Goal: Moore 35
Referee: Andrew Madley.
