The Dutchman's side soared to victory with help from the Cottagers' resident American and the Northern Ireland captain in a result that leaves Juande Ramos' squad all but beaten.
Aaron Hughes opened the scoring from close range after 38-minutes following a quiet start to proceedings, while the USA international netted his first two minutes before the interval before adding his second shortly after the break.
Martin Jol rested the likes of Andy Johnson and John Arne Riise for the weekend, as they joined Philippe Senderos on the bench, while Pajtim Kasami made his debut following his move from Palermo last month.
The first 15 minutes brought a couple of chances for Fulham, the first coming from Kasami’s shot powered straight at Jan Lastuvka and the second from Sidwell's header, which also failed trouble the visitors' goalkeeper.
Chances continued to prove thin throughout the half but the hosts finally did enough to break the deadlock through one of their many corners.
Damien Duff played the set-piece short to Matthew Briggs and the youngster placed a low cross from the touchline in front of goal for Hughes to lay a deft touch on the ball, putting it into the far corner.
It took just four minutes for Fulham to double their lead. Stephen Kelly pulled the ball back for Sidwell down the far right-side of the Dnipro area, and the midfielder followed up with a perfect cross for Dempsey to slot home unmarked.
After the break, Fulham started the second-half just as they had left the first and made it 3-0 on 49 minutes. Dempsey completed his brace as he met a well-flighted cross from Kasami with a powerful header.
Dnipro had yet to fully test the Fulham defence and could only force the odd corner out of Mark Schwarzer, from which they never threatened.
Juande Ramos’ side got their closest chance on 76 minutes after Nikola Kalinic danced his way through the Fulham defence and into the six-yard box, but the striker was overwhelmed with defenders and lost control of the ball which subsequently rolled to Schwarzer.
It could have been four to Fulham three minutes from time after Dempsey struck a drifting cross in for Kasami at the back-post, but the Swiss attacker slid in off balance and failed to hit the target.
Fulham continued to dominate the match and have left Ramos’ side with an uphill struggle on the return leg in the Ukraine.
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