Luton is still waiting for its first point after a 1-0 loss to Fulham in the Premier League on Saturday.
The newly promoted side extended its losing run to four games after substitute Carlos Vinicius’ 65th-minute winner for Fulham at Craven Cottage.
The result left Luton at the bottom of the table as it continues to struggle on its return to the English top flight for the first time since 1992.
With both teams trying to find a breakthrough, Fulham produced the decisive moment three minutes after Vinicius came on for Raul Jimenez in the 62nd.
Andreas Pereira found Willian out wide before the winger’s cross forced Luton goalkeeper Thomas Kaminski to parry the ball. It fell to the feet of Vinicius who, despite only just coming on, was sharp enough to convert.
Willian came close to doubling Fulham’s lead with a long-range effort and Vinicius had another chance late on, but could not add a second.