- Carlos Vinícius (65')
Fulham were far from convincing but did enough to move up to ninth in the standings while winless Luton are rooted at the bottom with a game in hand.
After a minute's silence for former club owner Mohamed Al-Fayed, who died last month, Fulham dominated possession in the first half but the home side had little to show for it and Luton came closest to opening the scoring.
Amari'i Bell nearly gave Luton the lead three minutes into the second half when he got on the end of a cross from Brown but his side-footed volley did not have enough power behind it and Bernd Leno made a comfortable save.
With the home fans growing frustrated, Fulham boss Marco Silva threw on Vinicius just after the hour mark and the Brazilian forward made an instant impact when he pounced on a spill from goalkeeper Thomas Kaminski for a tap-in.
Luton centre back and captain Tom Lockyer played up front in the closing stages and the 28-year-old found space for a free header in the final minute of stoppage time, but failed to find the target.
- Michael Salisbury
|Brighton & Hove Albion||15||7||4||4||+5||25|
|West Ham United||14||6||3||5||0||21|