Jason Koumas scored on his 300th league appearance to snatch an unlikely point for a below-par Wigan.
Koumas is flanked by two team-mates after scoring from the spot
On 11 minutes, Clint Dempsey got on to the end of a Diomansy Kamara cross and fired home to put Fulham ahead.
Wigan had already been rocked two minutes earlier when striker Emile Heskey was forced off injured.
After the break, Chris Kirkland saved well to deny Dempsey before Koumas confidently slotted home a penalty after Mario Melchiot had been fouled.
It secured a barely-deserved draw for Wigan, who huffed and puffed and also lived dangerously as Fulham made the better of the chances.
The hosts started well, winning a free-kick in a dangerous position in the opening minute but Paul Konchesky headed clear.
But Fulham soon responded, when Hameur Bouazza nipped in between Latics defenders David Cotterill and Melchiot, but he fired his low shot just wide of target.
Then Wigan - and possibly Steve McClaren - suffered a blow when Heskey, who had been given a rousing ovation by both sets of fans for his recent England exploits, limped off after only nine minutes.
On came Marcus Bent and he soon crossed for Antoine Sibierski to test Antti Niemi in the Fulham goal.
The action quickly moved to the other end and Fulham struck the first blow when Dempsey slotted home - Fulham's 100th goal in the top-flight.
And Fulham came close to extending their lead in the 25th minute when captain Carlos Bocanegra got on the end of a Simon Davies corner but could only bounce his header over the crossbar.
Wigan gradually began to take something of a grip on the proceedings but dreadful final balls ensured Niemi was never seriously being tested.
After the break, Fulham attempted to up the tempo and Kirkland was soon forced into a double save, first parrying Simon Davies' free-kick and then Aaron Hughes' shot.
And soon after, Fulham fashioned a superb chance when Dempsey exchanged a sweet one-two with Kamara but could not direct his shot wide of Kirkland's legs.
With the game petering out - and the ball spending more time up in the air than being passed around between players - Fulham might have thought they were about to secure their first Premiership win away from home this season.
But Bouazza put in a clumsy challenge on Melchiot in the area and Koumas comfortably dispatched the resultant spot-kick.
Wigan boss Chris Hutchings:
"We started very slowly, we didn't retain the ball and we didn't pass it. The second half was a little better and we showed more urgency.
"We got a result at the end of the day but it was not really deserved.
"They were a lot sharper and mentally brighter than us. It didn't help that we lost Emile Heskey, who has gone to hospital for a scan."
Fulham boss Lawrie Sanchez:
"It should have been an away win. We were in control of the game for 80 minutes. We should have added to our lead but we didn't take our chances.
"I think it was as comprehensive an away win as you could see, without us actually taking all three points.
"I'm bitterly disappointed that we have dropped two points."
Wigan: Kirkland, Melchiot, Granqvist, Bramble, Boyce, Cotterill (Skoko 60), Scharner, Brown, Koumas, Sibierski (Aghahowa 74), Heskey (Bent 9).
Subs Not Used: Pollitt, Hall.
Goals: Koumas 80 pen.
Fulham: Niemi, Baird, Hughes, Bocanegra, Konchesky, Davies (Murphy 84), Davis, Smertin, Bouazza (Ki-Hyeon 84), Dempsey, Kamara (Healy 67).
Subs Not Used: Keller, Stefanovic.
Goals: Dempsey 11.
Ref: Rob Styles (Hampshire).