Tim Oscroft, BBC Sport
Fulham's last outing came amid a turbulent few days for the Cottagers, with Joao Palhinha's proposed move to Bayern Munich collapsing at the end of the transfer window, before a painful 5-1 defeat by Manchester City.
That loss at Etihad Stadium left manager Marco Silva infuriated by the VAR decision that allowed Nathan Ake's goal to stand, but the Portuguese cut a calmer figure on the occasion of his 100th game in charge at Craven Cottage.
His recall of Palhinha, Fulham's player of the season during the last campaign, gave his side an early edge but they faded and looked short of ideas to combat Luton's resilience as the first half wore on.
But the double substitution, with Harrison Reed and Raul Jimenez making way for Alex Iwobi and Carlos Vinicius, proved to be crucial and gave them a cutting edge and creativity. Iwobi was involved in the build-up to the goal before Willian's chipped cross from the left which Luton goalkeeper Thomas Kaminski spilled into the path of Vinicius in the six-yard box.
Despite the single-goal advantage Fulham looked comfortable for much of the rest of the game, holding out to seal the win and their first home clean sheet in the league since beating Nottingham Forest in February.