It has been a season to forget so far at Craven Cottage, with a topsy-turvy campaign featuring far more troughs than peaks.
The Whites had looked to be heading towards almost certain relegation under Martin Jol, but successor Meulensteen is starting to steer the ship back on course.
There have still been bad points - notably a 6-0 mauling at Hull - but victory over West Ham on New Year's Day means another win against Sunderland on Saturday could propel them away from the bottom three.
"[That gap] is why it is hugely important," Meulensteen said.
"West Ham was hugely important, which we came out from really, really well. We had a great result and a good performance.
"Sunderland is likewise. It is a huge game for us, it is a huge game for them, but we are being positive, have been working well and working hard.
"The quality has been there and it is starting to pay off. Hopefully that will be the same against Sunderland tomorrow."
Such is the magnitude of Saturday's clash on the banks of the Thames that Sunderland manager Gus Poyet admitted the importance is not far off a cup final.
"I can see exactly where he is coming from, absolutely," Meulensteen said. "But it is 90 minutes-plus where you need to turn up.
"It is good for us that is played at home because it gives you that slight advantage with your own fans, so hopefully that will help us get the win."
The Black Cats head to west London buoyed by an impressive 2-1 Capital One Cup semi-final victory over Manchester United on Tuesday.
Fulham have also received a boost ahead of the match, with news that captain Hangeland could make his first appearance since the 4-1 win at Crystal Palace on October 21.
The 32-year-old centre-back underwent surgery in December to clear sciatic nerve trouble and is now back in full training with the Whites.
"Brede is coming with full training with us, so he is up for selection in that respect, so he has done really, really well and is progressing nicely," Meulensteen said.
"It is up for us to decide whether he is okay to start. We haven't made our mind up completely, but I am very happy that he is up there for selection.
"But when people come back from a long injury, the last thing you want is to come back and then go again. We want him to come and stay, so we will be very, very cautious."
Goalkeeper Maarten Stekelenburg could also return and will have an ankle complaint assessed before the match, while full-back Kieran Richardson is available after hamstring tightness to face his former club.
Bryan Ruiz may well be left out of the squad after Meulensteen confirmed the Costa Rica international can leave in January, with Real Betis and a return to Holland among the possible destinations.
One player the Dutchman has no intention of letting go, however, is Dimitar Berbatov, despite the continuing links to Arsenal.
Asked if he was resigned to losing the Bulgarian, Meulensteen said: "No, I am not resigned to anything.
"You can only resign to something when things happen and at this moment in time it hasn't. He is a Fulham player and a very important one for us.
"We would lose quality, experience, that special aspect that makes him stand out from the others.
"He can do things, turn things on, pull things out of the hat. He is an exceptional player."
Meulensteen was also quizzed about potential arrivals to Craven Cottage, ruling out a move for Brondby target man Simon Makienok and downplaying reports of interest in West Ham's Ravel Morrison.