Rovers picked up a crucial three points but were pushed all the way by Queens Park Rangers at Ewood Park.
Steve Kean's side were irresistible in the first half, leading at the break by three goals thanks to strikes from Yakubu, Steven Nzonzi and Junior Hoilett.
However as good as Rovers were in the first half, Rangers were equal in the second, substitute Jamie Mackie giving Rovers a nervy ending with two late goals.
But the home side held on to claim what could be a huge win come the end of season shake-up.
Following on from last weekend's heavy defeat at Arsenal boss Steve Kean made four changes.
There was a first start in a Rovers shirt for Bradley Orr against the side he joined from last month, Grant Hanley replaced the suspended Gael Givet at centre half, Mauro Formica replaced the injured David Dunn whilst Yakubu returned following his suspension with Anthony Modeste dropping to the bench.
The visitors made three changes with Fitz Hall, Akos Buzsaky and Armand Traore coming in for Shaun Derry, Djibril Cisse and Luke Young.
Roared on by a vocal home support Rovers started brightly, the lively Junior Hoilett impressing in the early exchanges.
But for all of Rovers' patient approach play, it was the tried and tested boot of Paul Robinson from which they took the lead. The Rovers captain sending the ball long into the Rangers half, Steven Nzonzi flicking on for Yakubu who finished emphatically.
The fans had only chanted his name seconds earlier and he repaid them with his 14th goal of the campaign.
At the midway point Rovers doubled their lead. Steven Nzonzi, who's slip on half way had allowed the visitors to attack, then started the move that saw him find Hoilett who, after tricking his way into the area, found the Frenchman and he drilled past Paddy Kenny into the back of the net to spark jubilant scenes on the pitch and in the stands.
Fulham responded with their best effort of the first half, Bobby Zamora hooking the ball narrowly wide after pressure from a corner, but it was Rovers who were next on the scoresheet in first half injury time as Morten Gamst Pedersen sent a free-kick on halfway into the penalty area to where Scott Dann headed across the area for Junior Hoilett to lash home via a deflection off the boot of Nedum Onuoha.
No doubt with the manager's half-time message ringing in their ears, the visitors came out a totally different side in the second. From the offset a side that had offered little as an attacking force in the first period were suddenly on the front foot causing all sorts of problems to Rovers.
Their threat came primarily down the right, with Shaun Wright-Phillips and Nedum Onuoha taking advantage of the space afforded to them, the home side just about surviving, important blocks from defenders and Paul Robinson keeping them at bays.
At the other end Yakubu showed the confidence of a man in form with an audacious strike from distance that beat Paddy Kenny all ends up but the ball crashed off the crossbar and away. It was a sumptious strike but just a couple of inches too high.
That proved to be brief respite for Rovers as the opposition again went close, Paul Robinson denying Onuoha before Taiwo found the side netting on the overlap.
With 19 minutes remaining Rovers saw their comfortable lead reduced. A mistake by Bradley Orr handed the ball to Taiwo and he crossed for substitute Jamie Mackie to convert from close range.
The home fans urged their side on but Rovers couldn't raise their game, Paul Robinson pouncing on the ball to prevent Mackie before beating away an Adel Taarabt effort.
Just when it looked like Rovers had quelled the danger than the nerves were raised further. Jamie Mackie turning brilliantly in the area to lash home an unstoppable effort with two added minutes remaining.
Thankfully Rovers saw the game out to claim their first win over a Mark Hughes managed side, but those two late goals meant they didn't climb out of the bottom three.
ROVERS: Robinson (c), Orr, Hanley, Dann, Martin Olsson, Lowe, Nzonzi, Pedersen, Formica (sub Modeste 67 mins), Hoilett (sub Henley 50 mins), Yakubu (sub Goodwillie 90 mins).
Subs not used: Bunn (GK), Petrovic, Rochina, Vukcevic.
QPR: Kenny, Hall (sub Gabbidon 90 mins), Taarabt, Traore, Buzsaky (sub Mackie 66 mins), Barton (c), Wright-Phillips, Taiwo, Ferdinand, Onuoha, Zamora.
Subs not used: Cerny (GK), Hill, Derry, Bothroyd, Smith.
Booked: Lowe (Rovers), Mackie (QPR).