Carlos Vinicius’ goal – scored shortly after he had come on as a substitute – gave Fulham victory at Craven Cottage.
Vinicius pounced to score after a mistake by keeper Thomas Kaminski, who weakly parried Willian’s cross.
Luton caused the Whites problems and had almost taken the lead when Issa Kabore’s right-wing cross was headed against the post by Jacob Brown.
And in stoppage time, Tom Lockyer missed a great chance to equalise for the Hatters when he headed another Kabore cross wide of the target.
Fuham’s second Premier League win of the season leaves them ninth in the table.
They struggled to create clear-cut chances but were better after Vinicius was introduced along with new signing Alex Iwobi, who came on for his debut.
Fulham: Leno, Tete, Diop, Ream, Castagne, Pereira (Cairney 81), Reed (Iwobi 62), Palhinha, Wilson (De Cordova-Reid 81), Jimenez (Vinicius 62), Willian (Bassey 90).
Subs not used: Rodak, Toure, Muniz, Francois.