A goal from Mohamed Salah from the penalty spot was enough to secure three points for the Reds.
Liverpool now have 59 points, which is four points behind fourth-placed Manchester United, who have two games in hand over them.
Fulham, on the other hand, are now in the 10th position on the league table with 45 points.
Converting emphatically from the spot to earn us all three points ? pic.twitter.com/3vMg0uyeUr— Liverpool FC (@LFC) May 3, 2023
Fulham started brightly and had the first decent chance of the game when Carlos Vinicius forced Alisson Becker into a save with a stinging shot that was turned behind for a corner in the 14th minute.
However, the game took a turn six minutes before half-time when Issa Diop's moment of madness saw Liverpool take the lead.
Darwin Nunez made the most of Diop's indecisiveness to poke the ball away and the defender hacked him down, with the referee immediately pointing to the spot.
Salah stepped up and smashed the resulting spot-kick straight down the middle to extend his streak of scoring in consecutive games at home to eight.
Fulham's best chance to equalise came when Vinicius broke through in the 77th minute but again Alisson thwarted him, using a strong right hand to deflect his close-range shot behind and ensure his side held on for a fifth straight Premier League win.