League Two Accy started brightly as Fulham struggled to cope with the difficult surface with Michael Symes and Sean McConville both testing visiting keeper Mark Schwarzer inside the opening ten minutes.
But it was Fulham who broke the deadlock against the run of play in the 21st minute. Duff's near-post corner was flicked on by Gera and Nevland stole in at the back post to toe-poke the ball under Stanley's Australian keeper Dean Bouzanis.
The home side were level four minutes later as Schwarzer failed to deal with a weak McConville strike and, after the ball ricocheted off Brede Hangeland, Symes was on hand to slide the ball home from close range.
Fulham continued to struggle and Robert Grant almost put Accrington ahead, but his well-struck shot from 20 yards was parried by Schwarzer before Hangeland hacked the ball to safety.
The game then turned dramatically in the visitors' favour two minutes before the break as Darran Kempson received his second yellow card after a late challenge on Nevland.
The Premier League side made their numerical advantage count just before the hour as substitute David Elm's quick free-kick was flicked on by Nevland and with the Stanley defence flatfooted, Duff ran through unchallenged to slot home.
It was one-way traffic from then on as Fulham bossed proceedings, Nevland forcing Bouzanis into a smart save after cutting in from the left and firing in a stinging right-footed drive.
Fulham's third of the afternoon arrived in the 80th minute as Nevland fed Bjorn Helge Riise on the right and the Norwegian's cross was tapped home by Gera to complete a textbook counter-attack from the top-flight outfit.