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 have closed the gap to Newcastle 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.
"Massive win. I loved Scott Parker's reaction there," former Aston Villa striker Gabriel Agbonlahor told talkSPORT. "Those sort of games today are a must win. You have to win and credit to all the players and Scott Parker.
"If you're Newcastle, Brighton, Burnley or Crystal Palace now you're looking behind your back."
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.
The Blades 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.
Less than five minutes later, the visitors had their first shot on target, with Alphonse Areola just denying Enda Stevens with his legs in a one-on-one situation.
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.
Fulham claimed a vital 1-0 Premier League victory over rock-bottom Sheffield United to close the gap on survival to just three points.