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.
1. Simon Sluga 8
The keeper pulled off five top drawer saves, including three in quick succession in the first half. May feel disappointed to have saved well from Aboubakar Kamara only to see Bobby Decordova-Reid pounce late on
2. Ryan Tunnicliffe 6
Worked hard but should have notched his first goal Luton when he found himself one-on-one with goalkeeper Marek Rodak, though he still managed to keep the chance alive with Harry Cornicks shot getting blocked
3. Sonny Bradley 6.5
Aggressive tackling, having been too far off Fulhams forwards at Craven Cottage, but he wont be happy with conceding three from aerial crosses into the box
4. Matty Pearson 6
Good on the ball and looked to burst forward in possession, but was caught out for the first and second goals with Bobby Decordova-Reid and Aleksander Mitrovic giving him the slip