Pascal Chimbonda's dramatic injury-time header earned Wigan their fifth successive win in the Premiership.
The Frenchman finished off Graham Kavanagh's cross, but it was harsh on Fulham who impressed during the game.
Tomasz Radzinski and Steed Malbranque shot wide for Fulham who thought Latics keeper John Filan should have been sent off for handling outside the box.
Henri Camara shot into the side-netting late on for Wigan but there was still time for Chimbonda to win the match.
The victory was Wigan's seventh in a row in all competitions but it scarcely seemed possible after a first half in which Fulham dominated.
The Cottagers began with a flourish and Radzinski and Malbranque's shots both missed by inches and came within the opening four minutes.
Radzinski's left-foot shot whistled past the post before Malbranque weaved into the box and curled a shot just wide, with Filan beaten.
The home side came close when Damien Francis was only just unable to connect with Ryan Taylor's header back across goal on 13 minutes, when a touch would have put the ball in the net.
But Wigan, without the injured Jason Roberts, were toothless and Fulham's Pape Bouba Diop was unfortunate with a looping header which dropped on to the roof of the net.
Shortly afterwards, Wigan keeper Filan raced outside his box to intercept Fulham's Collins John and the Dutch striker's shot hit the Australian's hand after rebounding off his knee.
Referee Andre Marriner did not give a free-kick - much to the fury of Cottagers boss Chris Coleman, who believed Filan should have been sent off.
The Welshman's mood did not improve as Moritz Volz was booked for diving - when replays suggested he had been impeded by Wigan's Alan Mahon just outside the box.
Mahon had earlier sent a powerful volley narrowly wide of the post but the Latics were some way below their best in the first half.
Wigan boss Paul Jewell said before the game that this represented Wigan's toughest match so far this season and Fulham's first-half display backed up his prediction - and the London side continued to dominate possession upon the resumption.
But chances were at a premium in the second half and it was Wigan who were first to fashion a clear opening, substitute Andreas Johansson heading over from Taylor's cross.
But Fulham keeper Tony Warner was given little to do and the home side appeared to have missed their chance of victory in the dying minutes as Camara skipped past Carlos Bocanegra and Warner only to fire into the side-netting.
But with seconds to go, Chimbonda's late strike won the match.
Wigan manager Paul Jewell:
"I am just relieved really.
"We were poor in the first half but in the second, without hitting any heights, we worked really hard.
"Fulham will be disappointed but my players deserve enormous credit for sticking at it when they were out on their feet. It is a great three points."
Fulham manager Chris Coleman:
"I hope he (Marriner) can sleep tonight because I won't be able to.
"You can't keep getting major decisions wrong, with these all within the first 45 minutes. It's hard, and everybody gets one wrong, but three or four?
"I had to change my team talk at the break. Rather than saying 'well done, keep going, you are doing well', I had to try and calm them down."
Wigan: Filan, Chimbonda, Henchoz, De Zeeuw, Baines (McMillan 74), Taylor, Kavanagh, Francis, Mahon (Johansson 62), Bullard (Teale 84), Camara.
Subs Not Used: Jackson, Pollitt.
Goals: Chimbonda 90.
Fulham: Warner, Volz, Bocanegra (Rosenior 90), Goma, Niclas Jensen, Claus Jensen (Elrich 82), Diop, Boa Morte, Malbranque, John (McBride 82), Radzinski.
Subs Not Used: Helguson, Batista.
Ref: A Marriner (W Midlands).