Pogrebnyak was drafted in on transfer deadline day to fill the void left by Bobby Zamora's move to QPR, but few could have predicted the impact the Russia international would make.
The 28-year-old gave the Cottagers a 36th-minute lead by heading home a Damien Duff corner, before hitting an exquisite second as half-time approached.
Fulham continued in the same vein in the second period and, after Dempsey's effort put them on course for a third successive league win, Pogrebnyak bundled home his third of the afternoon.
Dempsey netted Fulham's fifth in the 83rd minute to leave Wolves with just one win in 13 league games.
Fulham dominated from the outset and Ronald Zubar was soon booked for clattering Duff on the edge of the box.
Dempsey then outpaced Zubar to test Wayne Hennessey before the Wales international goalkeeper palmed away a low 20-yard drive by John Arne Riise.
Duff was the next to come close with a fierce shot from the edge of the box that went just wide after an impressive counter-attack.
Wolves were having to withstand a barrage of attacks in an opening 20-minute spell that was made worse when midfielder Karl Henry limped off to be replaced by Nenad Milijas.
The Serbian's introduction began a spell in the ascendancy for the Black Country side, who would have taken the lead had Richard Stearman's header from a Jamie O'Hara free-kick been slightly more accurate.
Brede Hangeland was booked for a late challenge on O'Hara as Terry Connor's side continued to press, with Riise reacting well to clear a goalbound Kevin Doyle header.
However, Fulham enjoyed the lion's share of possession and should have taken the lead moments earlier through Andrew Johnson, but Hennessey somehow blocked with his legs.
The home side's dominance eventually translated into the opener in the 36th minute, although in somewhat controversial circumstances.
Mousa Dembele, who had been Fulham's most impressive player in the first half, worked space for a shot which referee Mike Jones felt had brushed off Stearman on its way wide.
Stearman was unhappy with the decision but Duff whipped in the resulting corner for Pogrebnyak to head home from close range.
Pogrebnyak doubled Fulham's advantage eight minutes later after Fulham made the most of an awful cross-field ball from Milijas.
Dempsey chased it down and the ball was worked wide to Johnson, who teed up Pogrebnyak to fire home with aplomb.
Fulham continued in the same vein in the second period and were unfortunate not to add to their lead after a defensive mishap between Christophe Berra and Hennessey allowed Johnson to square.
Nobody was in the Wolves box to meet the ball but, after Dempsey saw an effort saved, Fulham did manage to eke out a third.
Danny Murphy's sublime pass was collected by Dempsey and he rounded the goalkeeper to slot home.
Connor brought on top scorer Steven Fletcher, but moments later Hennessey was picking the ball out of his net once more.
The Welshman could not get hold of a Johnson shot, which squirmed out of his grasp allowing Pogrebnyak to complete his hat-trick in the 61st minute.
While Wolves were managing the odd attack, the home side were in control and Johnson hit the crossbar with a curling right-footed shot.
Fulham manager Martin Jol handed former Real Madrid midfielder Mahamadou Diarra his debut with less than 20 minutes remaining.
Murphy made way but there was no let up in attacking intent as Dembele saw a shot blocked by Berra, who was booked shortly afterwards for a foul on Johnson.
Dembele, Duff and Dempsey all had attempts on goal before the latter scored his second of the afternoon after connecting with a Diarra pass in the 83rd minute.