This was far from the routine victory for the Premier League team that the scoreline suggests. Roy Hodgson, the Fulham manager, certainly accepted that his side were in trouble against their League Two opponents before Accrington were reduced to 10 men shortly before half-time.
Perhaps the extra quality of Fulham would still have edged out a full-strength Accrington team, but the exchanges before Darren Kempson's dismissal suggested otherwise.
The scores were level at 1-1 when Kempson, who had already collected a yellow card, scythed down Zoltan Gera from behind and totally changed the complexion of the tie.
John Coleman, the Accrington manager, was not happy with the performance of the referee, Stuart Attwell, but Kempson's challenge was foolish and Hodgson had little sympathy.
He said: "Red cards do change games. It is much harder than playing with 11, so you have to make sure you don't commit fouls that merit yellow cards."
The managers were more united on the way Accrington approached this formidable task. Hodgson said: "Give Accrington credit. We didn't adapt very well to the conditions at the beginning and the number of balls they whacked into our final third surprised us. They made it difficult for us to get those balls out and pinned us back for long periods."
Fulham knew even before the start that this would be no ordinary day at the Premier League office. One glance at the sloping, bumpy Crown Ground pitch and a committed crowd indicated why Hodgson had taken no chances with his team selection.
He fielded virtually his first-choice team – it was certainly stronger than the one he fields in the Europa League – and they quickly found out why Accrington are rated as one of the most improved teams in League Two. With nine minutes gone, Stanley were nearly rewarded for their tidy and intelligent approach with a shot from Michael Symes that Mark Schwarzer saved at full stretch.
The Australian keeper then produced an even better response when Sean McConville took advantage of dreadful marking by the Fulham defence. It was a hugely encouraging start for Stanley, whose financial difficulties were illustrated by a banner reading, "Love Stanley, Hate the Taxman".
Partly thanks to their Cup run, the cash crisis has eased since they were the subject of two winding-up orders last year. And those opening exchanges suggested players such as Symes and Robert Grant may generate some more income from interested clubs.
Fulham, though, went ahead with their first attack after 21 minutes. A corner was touched on by Gera and Erik Nevland was able to knock it in from close range. To their credit, Stanley responded within four minutes and Schwarzer was at fault as he failed to cling on to a deflected shot that was going out for a corner. McConville latched on to the loose ball and his shot was saved on the line by Brede Hangeland before Symes drove it in.
Grant again troubled Schwarzer before the turning point when Kempson was dismissed. "We only need 10 men," chanted the Accrington fans and, for a while, it seemed they might be right before Damien Duff put Fulham ahead in the 59th minute. Accrington failed to find any response this time, and leaked another goal when Gera scored.
Coleman said: "We gave a good account of ourselves and I can't be too harsh on my players because we were down to 10 men. I know Fulham will not have had to soak up so much pressure for half an hour, so we have to take credit for that, but I'm never happy when we lose.
"It's all about winning and losing. It's nice to say we played well, but we're disappointed we lost."
Referee: Stuart Attwell
Man of the match: Ryan
Match rating: 7/10