Ademola Lookman broke the deadlock for the Cottagers in the 61st minute, with the home side going on to secure only their fourth win of the season.
Scott Parker’s men went into the game six points adrift of Newcastle but have closed the gap to just three, ahead of the Magpies’ trip to Manchester United on Sunday.
Sheffield United, rooted to the foot of the table, struggled to really trouble in-form Fulham.
The game started quickly from both sides, with the noise from the dugouts adding to the tension of what seemed a must-win game.
The Blades looked more dangerous from set-pieces, but Fulham, as has been the case on many occasions this season, struggled to really test Aaron Ramsdale in the United goal.
Chris Wilder’s men were penned back into their own half for much of the opening 45 minutes, but defended resolutely, with a number of well-timed trips in the midfield preventing Fulham from building up momentum.
Fulham’s stand-in captain in the long-term absence of Tom Cairney, Joachim Andersen was a commanding presence at the back, not only in organising the defence but with his well-weighted long balls to the front players.
Harrison Reed had a shot from distance straight at Ramsdale, with the goalkeeper also in the right place to deny Lookman.
United went into the half-time break without a touch or attempt in the Fulham box but were doing a good job of defending their own, and got men behind the ball to break up the home side’s attacks.
At the start of the second half, Ruben Loftus-Cheek came close to giving the home side the lead when he weaved his way through the United defence before his goal-bound shot hit Ramsdale’s outstretched leg and was cleared off the line by George Baldock.
Lookman put the hosts ahead just after the hour mark with his fourth goal of the season, and his second against the Blades.
The 23-year-old worked his way into the area from the left-hand side before firing a low drive past Ramsdale and into the back of the net.
United had a penalty shout in the final minutes of the game, when Areola dived out to deny Jayden Bogle. The goalkeeper put his body on the line and just managed to get a touch on the ball before the collision.