The Cottagers snatched a share of the spoils with their third equaliser in the fourth minute of stoppage time.
That late, late strike, coupled with Stoke City's last-gasp winner in their clash with Sheffield Wednesday, means Graeme Jones' side dropped into the bottom three of the Sky Bet Championship.
To see how the Hatters players rated on the day, see below.
5. James Bree 6
Set up James Collins for his goal with a brave header and didnt do much wrong in defence, but the crosses from Fulhams first and third goal, came from his side of the pitch | Getty
6. Callum McManaman 7
Perhaps overshadowed by Kazenga LuaLua, but the winger came back into the side and was sharp in attack and dogged in his defensive duties. Understandably disappointed to be subbed on 65 minutes | Getty
7. Luke Berry 7.5
Put in a tremendous shift. Luton were tasked with operating a high press and Berry picked Joe Bryans pocket to set up Harry Cornick for Towns third goal. Good on the ball too | Getty
8. Pelly-Ruddock Mpanzu 7
Was always involved in the thick of the action and could often be found breaking up play and looking to start an attack | Getty