Allardyce is undergoing heart surgery on Friday and was told not to follow the game from his sick-bed - and it was probably just as well after his side failed to turn up and a goal from Erik Nevland and two from Clint Dempsey sealed Fulham's win.
The three points lifted Roy Hodgson's side up to tenth, but after the opening 40 minutes the vast majority inside a freezing Craven Cottage would surely have agreed that neither team deserved anything from the game after what had been a turgid game.
That all changed, though, when Nevland slotted home just before the break, and Fulham were much improved after the interval as Dempsey made the game safe with 20 minutes remaining and added a third late on.
Allardyce had picked the Blackburn XI and decided to play with both Jason Roberts and Franco Di Santo up front, but he would have been disappointed by their impact.
Di Santo had Blackburn's only clear chance of the entire game after just 90 seconds, though, being denied by Mark Schwarzer after Keith Andrews had put him through.
From there the game degenerated into aerial ping-pong, with the home fans not afraid to show their displeasure at the lack of adventure on offer.
But with time running out at the end of the half Fulham took the lead through their only coherent passing movement.
Nevland was at the heart of it, playing one-two's with first Bobby Zamora and then Damien Duff, before latching on to the latter's astute pass and firing inside Paul Robinson's near post.
It was a lead the hosts did not deserve, but they made the most of their good fortune, putting in a much improved display in the second period.
Chris Baird had come closest to doubling their advantage, his low drive causing Robinson to spill the ball, but it was Dempsey who scored the all-important second with 20 minutes to go.
Again Duff, who played all 120 minutes in Ireland's heart-breaking World Cup qualifying defeat to France last week, was at the heart of the move as he cut inside and fired at goal, the shot taking a deflection to land perfectly at the feet of Dempsey, who fired home despite vociferous appeals for offside from the visitors.
Nevland then somehow missed when Dempsey put him clean through, but it always seemed unlikely that Blackburn would trouble Schwarzer again, let alone score twice more.
And Fulham put the game completely beyond their visitors when Dempsey scored his fifth Premier League goal in as many games.
Simon Davies was the creator this time and Dempsey controlled the Welshman's cross before finding the bottom corner to make Allardyce's evening even more miserable.