Rovers boss Allardyce is scheduled have an operation on a coronary artery and could be back next week – and despite the scoreline he is certain to highlight the clash at Craven Cottage as a missed opportunity.

Rovers goalkeeper Paul Robinson did not have a save to make until Erik Nevland squeezed a finish in at the near post after 43 minutes, and the game was still up for grabs until Dempsey tapped in with 23 minutes remaining.

He then grabbed his second before the end meaning the visitors failed to build on their win over Bolton at the weekend.

After three matches without a victory, Fulham moved above their opponents and into the top half of the table, although maximum points looked unlikely during a first half short on quality.

Blackburn had not lost to Fulham since 2005 and within two minutes they had a chance to claim an early advantage.

Keith Andrews, a replacement as Brett Emerton had a knee injury, weighted a ball through the home defence, Franco di Santo got on the wrong side of Aaron Hughes but Mark Schwarzer stood up well and blocked the finish.

Fulham’s response was a direct move that saw Bobby Zamora hold the ball up, Damien Duff cross to the far post and Dempsey head wide while under pressure from Blackburn’s physically imposing defenders.

It was hardly inspiring play from either team, both sending long balls forward that amounted to nothing.

Jason Roberts at least created one chance when he brought a punt down, with El-Hadji Diouf crossing and Di Santo stabbing over.

Di Santo also failed to get power on a close-range header after David Dunn’s free-kick was nodded into the danger area – but it was not much to warm up the freezing fans at Fulham’s stadium by the Thames.

The supporters tried to liven things up with a hopeful penalty shout when Ryan Nelsen chested the ball in his area, but referee Stuart Attwell waved play on and there were no complaints from Fulham players.

Roberts tried his luck with a turn and shot, although Schwarzer saved easily. The Rovers striker also curled wide just before the opener.

Nevland’s goal came two minutes before the break and was totally at odds with the 43 before it.

Zamora sparked the slick move by backheeling to his strike partner, Nevland then exchanged passes with Duff before setting his sights from the right side of the area.

Robinson had not been required to save up to that point – and he would have been disappointed with Nevland’s finish going in at the near post for the Norwegian’s second of the season.

Encouraged by their unexpected lead, Dempsey could have doubled the advantage three minutes after the restart when Jonathan Greening swung over a free-kick. But the American headed wide.

Chris Baird, anchoring the midfield rather than in defence, forced Robinson into his first save of the match with a 25-yard shot in the 57th minute, after he had turned sharply away from Vince Grella.

Rovers attempted to force an equaliser with a set-piece that Di Santo headed just wide – but that was his final contribution as Neil McDonald, in charge while Allardyce is away, changed both of his strikers.

Roberts also came off, with Nikola Kalinic and Benny McCarthy coming on, but Fulham struck straight after the double swap.

Duff ran at full-back Pascal Chimbonda and curled in a cross that split the Blackburn defence and allowed Dempsey to tap in.

Nevland raced through but finished wide when most of the ground thought he had added a third, while at the other end Kalinic was guilty of a blatant dive in the penalty area but did not fool Attwell.

Dempsey’s second came just before the final whistle. He collected Simon Davies’ cross at the near post, held off Andrews and slotted past Robinson.