It appeared that the hosts from League One would win through when Chris Porter put them in front before the break.
However, the tie turned on the sending off of United skipper Michael Doyle after the restart and Fulham went on to force a replay courtesy of a low strike from Hugo Rodallega.
You can find out how the tie unfolded with our minute-by-minute updates below.
12.01pmAfternoon all. So, after a number of ties over the last couple of days, the fourth round of the FA Cup concludes today. Here we will be covering Fulham's trip to Sheffield United.
12.03pmBut hang on, we may have a problem. The wet conditions have left the Bramall Lane pitch somewhat soggy. Referee Andre Marriner is expected to carry out an inspection shortly, but worryingly the rain is still falling. We will keep you posted.
12.06pmDue to the uncertainty over whether or not this tie will take place, the team news has not yet been released. According to officials, if the game is to go ahead, both mangers will submit their team sheets in around 10 minutes.
12.10pmWell, it appears that we have some good news:
The pitch has passed the 12noon pitch inspection. Referee Andre Marriner says #FACup tie with Fulham will start. #sufc#twitterblades
12.18pmSo, it's a 4-4-2 formation from Sheffield United boss Nigel Clough, who has partnered Chris Porter and Jose Baxter in attack. There is also a place at full-back for Cardiff City loanee John Brayford, while Michael Doyle and Ryan Flynn feature in a four-man midfield.
12.24pmFULHAM SUBS: Stekelenburg, Pritchard, Christensen, Kacaniklic, Taarabt, Plumain, Bent
12.27pmWell, it seems that Fulham manager Rene Meulensteen has one eye on Tuesday's Premier League clash against Swansea City. He's made a host of changes, including handing a full debut to young defender Josh Passley. There is also a first start for attacker Muamer Tankovic. The likes of Damien Duff, Giorgos Karagounis and John Arne Riise will provide the experience.
12.31pmAs his team selection suggests, Meulensteen has confirmed that Premier League survival is more important to him than success today. Here is some of what he has had to say: "The Swansea game is more important because it is so tight in the Premier League.
"There is not one country in the world that would let someone play in a fourth round of the cup on a Sunday and then play an important league game on Tuesday."
12.35pmWith Fulham's starting lineup in mind, would a Sheffield United victory be a big surprise today? Of course the away side do have some experience in their lineup and there are two divisions separating the teams, but you never know. In these conditions, with the home crowd behind them, the League One outfit may well fancy their chances.
12.39pmOf course, the Blades have already beaten a Premier League side in the FA Cup this season, following their success over Aston Villa last time out. Talking about that clash and this one, United boss Clough has said: "Finances are always important but it's about more than that. Whatever we've made from Villa Park and this game against Fulham, the glory of the day and winning is the main thing."
12.44pmWe know that Meulensteen sees this game as a distraction, but he is still keen for his team to get the win. Here's what he has just had to say to BT Sport: "I warned the players they can't be complacent," said Fulham manager Rene Meulensteen. "I said that to them straight away [after the draw].
"This will be a very difficult game. Sheffield United will try to chase everything and the crowd will get behind them. The key for us is to make sure we remain calm and focused and play away from that sort of pressure they throw at you."
12.48pmHaving just seen close up shots of both goalmouths, they are not in a good state! It's extremely muddy and as a result the goalkeepers have been asked to warm-up away from the nets. With the rain falling heavily, you cannot help but feel that it's only going to worsen.
12.52pmPREDICTION: Right, with only a few minutes to go until we get started, let's have a go at guessing the outcome of this tie. It's got to be said that everything is set up for an upset here. The weather, crowd and Fulham's team selection - surely Sheffield United have a good chance of reaching round five. Let's go for a 2-1 win to the hosts.
12.56pmHere come the players to a big cheer from the supporters. Will we see a shock? Not long until we find out.
1 minKICKOFF! Hosting United, attacking from right to left, get this FA Cup round four tie off and running.
4 minSome smart early football from the home side, who in Brayford have a defender that likes to get forward whenever possible. Moments ago his cross fell to Porter, but he couldn't control the ball inside the area and Riise hacked cleared the danger. Positive from the hosts.
7 minNow it's Fulham's turn to play some good football as Tankovic and David exchange passes inside the United area, but the latter overruns the ball and ends up tripping up over the advertising hoarding. Thankfully he is fine and shows no sign of pain.
11 minSUBSTITUTION: Fulham are forced into an early change as Riise picks up a muscular injury during a challenge with Flynn. He immediately signalled to the bench that he couldn't continue. On in his place is French youth international Ange-Freddy Plumain, which means that Fulham now have inexperienced full-backs on both flanks.
15 minIn fact, Fulham boss Meulensteen has dropped the experienced Duff to full-back, with Plumain operating in a more advanced wide role. It seems that the manager was wary of his team having two defenders with very little experience.
19 minThe left corner flag towards the end that United are attacking is in shocking condition! It's pure mud, so the ball is sticking. Kasami and Murphy have just been involved in a bit of battle down there, with neither of them able to get the ball under control!
24 minCHANCE! United frontman Baxter has just summed up this tie so far. After Aaron Hughes fouled Porter on the edge of the Fulham box, Baxter had a decent chance from the resultant free kick. His effort was poor to say the least, though, as the ball flew wide of the target.
26 minMadness! Fulham goalkeeper David Stockdale has just conceded a corner because he couldn't stop sliding as he pounced on a loose ball. The rain is coming down extremely heavy now and at the moment you have to fear that this tie might end up being abandoned.
30 minNow up the other end the conditions have played a part as the ball stopped dead inside the six-yard box, just as Rodallega waited for a tap-in. Thankfully, though, the rain has just stopped.
31 minWhere has that come from?! The hosts have barely threatened at all, yet they lead. It's all about centre-back Maguire, who brings the ball out from the back and soon finds himself inside the Fulham area. From there, he drills the ball across for Porter, who gets between Hughes and Senderos to poke the ball beyond Stockdale for his fifth goal of the season. Do we have an upset on the cards?
33 minPENALTY APPEAL! An immediate response from the West Londoners and they want a penalty. Rodallega goes around George Long, but at the final moment he is clipped by the United goalkeeper. The appeals go up from the Colombian striker and his teammates, but Marriner is not interested. A lucky escape for the home side, who keep hold of their lead.
38 minThat goal has breathed some real belief into the home side. They have started to pass the ball around well, with Baxter and Porter up front showing some real signs of an understanding.
43 minUnited are defending deeply right now, which is making it very hard for Fulham and Rodallega in particular to get behind them. They need a bit more invention, perhaps down the flanks or from the centre of midfield.
45 minThere will be one minute of stoppage time at the end of this first half.
1.51pmMarriner blows for the break after Maguire receives treatment for a knee injury and it is the hosts that hold a one-goal lead in a tie that has been played in challenging conditions.
1.55pmThe statistics show that United have had just 27% of the possession during that first half, yet they hold the one-goal advantage. Despite that, Clough will probably be urging his players to take more care when they do have the ball. On the plus side, Baxter and Porter have given the Fulham defence problems on occasions, while up the other end the they have defended well.
1.58pmAs for Fulham, they have had just two shots (none on target) to show for their 73% share of the possession. They are really lacking invention in the final third of the pitch, particularly because the United rearguard is sitting so deep. Attacking down the flanks may represent their best chance of getting back into this contest.
2.01pmLooking at the Fulham bench, they do have options. Alexander Kacaniklic, Adel Taarabt and Darren Bent could all potentially make a difference. Remember, though, the early need to replace the injured Riise means that Meulensteen has just two substitutions left to make.
46 minSECOND HALF UNDERWAY! Fulham gets us restarted, while the hosts have made a change. Goalscorer Porter has gone off with a tight hamstring and has been replaced by midfielder Stefan Scougall, who only recently joined the club from Livingston.
49 minSAVE! Bright start from Fulham as Kasami forces Long into a save from 20 yards out. Then, there is more bad news for United as their centre-back Maguire limps off with a leg injury that he picked up late in the first half. He's been replaced by Bob Harris, with Hill moving into the heart of the defence.
53 minThe United skipper has been handed a straight red card by Marriner, who must have spotted his clash with Fulham's David off the ball. It seemed that Doyle kicked out at the youngster, following a clash between the two a couple of minutes earlier which left the United midfielder with blood on his face. It's not been the best of starts to this second half for the home side!
55 minSAVE! They be a man light, but it's United that are mounting the attacks. Flynn shows great pace to move into the area, before jinking his way beyond Hughes. That leaves him with just Stockdale to beat, but from a narrow angle, the Fulham keeper saves with his feet.
58 minSUBSTITUTION: Having been involved in the Doyle sending off, David has now been taken off. He's been replaced by striker Bent. It appears that Meulensteen is looking to make his side's numerical advantage count.
62 minCHANCE! This United side are set up to counter-attack and that is what they are doing really well at the moment. Hughes backs off Baxter 25 yards from goal, allowing him the space to shoot. Not that the striker needs an invitation as he attempts to curl an effort goalwards, but the ball bounces a couple of feet wide of the target.
67 minSUBSTITUTION: Not the nicest moment for youngster Plumain, who having replaced Riise earlier on in the tie, has now been taken off. On in his place comes Taarabt - Fulham need him to have his head screwed on to today.
72 minPENALTY APPEAL! Big shouts for a penalty from the home side as Flynn goes to ground following a challenge with Hughes. Replays suggest that there was contact, but not for the first time today, Marriner waves play on. It's a decision that has infuriated Clough, who has just had a talking to by the match official.
74 minKasami's influence is starting to grow in this game. He's looking to get on the ball whenever possible and although his shooting has been wayward so far, those that remember his strike against Crystal Palace earlier in the season know what he is capable of.
75 minFulham have been applying some pressure in recent minutes and now they have been rewarded. Some neat passing involving Taarabt and Tankovic tees up Rodallega on the edge of the United box. Having taken one touch to steady himself, the Colombian then proceeds to drill the ball beyond the reach of the Long in the home goal. Can the Londoners go on to win the tie now?
77 minBOOKING! It's a debut caution for Passley, who brings down Murphy in full flight. The youngster can have little complaint about that decision.
81 minBOOKING! Another Fulham player goes into the book and this time it's Kasami, who slides in late on midfielder Conor Coady.
83 minCROSSBAR! So close for Fulham, as United live dangerously. Senderos, up from the back, found himself unmarked as he looped a header goalwards. Long is beaten, but the ball cannons back into play off the crossbar. The rebound drops to the Fulham defender, but his second effort is crowded out and the home team eventually clear the danger.
85 minSUBSTITUTION: The hard-working Baxter is given a breather as Clough makes his final change of the tie. On in his place is former Watford midfielder Stephen McGinn.
88 minCHANCES! What an unbelievable chain of events and how are Fulham not leading? Senderos is again up from the back and sees a shot float wide, only for Kasami to head the ball across goal when he should have scored. It drops for Bent, who completely scuffs his effort despite having the goal at his mercy. His blushes are spared by the linesman's flag, but both Senderos and Kasami before him fluffed big chances.
90 minThere will be four minutes of stoppage time for one of these two sides to find a winning goal. Will there be late drama?
90+3 minCHANCE! Taarabt goes mightily close with a swerving effort from 25 yards out that takes a wicked deflection. Long is diving at fresh air, but thankfully for him and the home side, the ball drops inches wide of the target.
2.55pmOn what was a poor pitch, credit must go to all the players because they served up a very watchable FA Cup tie, particularly during the second half. What's more, they will now have to do it all over again at Craven Cottage next month for the right to progress through to round five.
2.56pmThat's all we have time for from Bramall Lane. Thanks for joining us this afternoon and until next time, goodbye.