The United States international followed up his first half effort with a header shortly after the restart to help Martin Jol's side to an impressive victory against Juande Ramos' side.
The Spaniard replaced Jol as Tottenham manager four years ago but the Dutchman managed to exact some revenge at Craven Cottage.
While Dnipro looked a sturdy outfit in the first period, Aaron Hughes' sucker punch as half-time approached was the first of three goals they conceded in 10 minutes.
Dempsey struck either side of the break to extend Fulham's advantage, while resolute defending meant the visitors were unable to find an elusive away goal.
Heading into the match, Jol made four changes to the side held to a 0-0 home draw by Aston Villa in Saturday's Barclays Premier League opener.
Matthew Briggs, Steve Sidwell and Stephen Kelly were drafted into the starting line-up, while summer signing Pajtim Kasami was handed his first start for the Cottagers.
Dnipro, meanwhile, started former Blackburn striker Nikola Kalinic and goalkeeper Jan Lastuvka, who had a loan spell at Craven Cottage in the 2006-07 season.
The Czech keeper was first called into action in just the fourth minute when the onrushing Briggs latched onto an exquisite ball from Brede Hangeland to unleash a near-post drive.
Steve Sidwell tested Lastuvka again from a corner but neither side looked particularly dominant in the opening exchanges.
Dnipro were proving a stern test for the home side, who were struggling to break down their resilient defence from both set-pieces and open play.
That said, neither side were utilising possession effectively and failed to build sustained attacks.
Kalinic looked a rare attacking threat for the visitors, who were behind in the 39th minute thanks to an unlikely source.
Giuliano's untimely slip allowed Briggs to dart to the byline and send in a low cross that Hughes nudged home.
Fulham doubled their advantage in the 43rd minute as Dempsey ghosted into the box to slot home Sidwell's right-wing cross.
The west Londoners started the second half in the same form as they ended the first, with Dempsey heading home Kasami's dinked cross four minutes after the restart.
Dnipro looked visibly shell-shocked after conceding but soon turned their attention to grabbing a potentially all-important away goal, with Ievgenii Konoplianka twice coming close.
The shots seemingly acted as a catalyst for the home side, who unleashed a barrage of attacks on the home goal and came close through Denys Kulakov's fizzing 20-yard effort.
Despite the visitors' pressure, Bobby Zamora should have made it 4-0 in in the 74th minute. Kelly unleashed a superb right-wing cross but the England international somehow managed to turn his shot over the bar from six yards out.
The effort punctuated a strong spell for the visitors, for whom Kalinic continued to threaten in attack.
Evgeni Cherberiachko forced Mark Schwarzer into a low save as the clock wound down, while Kalinic, Vitaliy Denisov and Serhiy Kravchenko all came close.
Dempsey almost netted his hat-trick goal with minutes remaining but more pertinently Fulham's defence remained resolute to the disappointment of the raucous visiting support.
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