Clint Dempsey scored the others as Terry Connor suffered his first defeat since taking charge of Wolves.
The end-to-end nature continued and a goal came after 36 minutes by Pogrebnyak, who was afforded too much space at the back post to dive forward and head home a corner.
After the break Martin Jol's side continued to aggress and Dempsey made it three by rounding Hennessey after an inch-perfect Danny Murphy through ball.
Pogrebnyak had his hat-trick in the 62nd minute when Hennessey could only parry Johnson's shot and Pogrebnyak was on hand to poke home.
Wolves's misery was compounded seven minutes from time when new signing Mahamadou Diarra found Dempsey, who fired home with his left.
The win means that Fulham have won three league games on-the-bounce for the first time since the 2007-08 season.
Three points moves the Cottagers up five places to eighth while Wolves drop into the bottom three after falling behind Blackburn on goal difference.