The Cottagers put in a confident performance in their first fixture since Hodgson swapped Craven Cottage for Anfield, with American Eddie Johnson and Zoltan Gera among their best performers.
Fulham were without their World Cup players and injured Andy Johnson, but still named a relatively strong line-up for the match, which doubled up as the testimonial for Bees skipper Kevin O'Connor.
Damien Duff, Brede Hangeland and Paul Konchesky were all named by temporary boss Ray Lewington, who saw his side tear into their League One opposition from the start.
David Elm should have put Fulham ahead in the third minute but he sent a point-blank header wide.
Leon Legge then denied livewire Johnson inside the box before Chris Baird broke the deadlock with a 25-yard low drive which beat off-balance Brentford stopper Richard Lee after 14 minutes.
The Bees were handed a way back into the game seven minutes later when Stephen Kelly clumsily fouled Charlie MacDonald in the box. Referee Keith Hill pointed to the spot but David Stockdale saved the striker's drive.
Brentford were made to pay for the miss soon after when Elm curled a 20-yard strike inside Lee's right-hand post to double the visitors' lead.
Duff raced through to poke past Lee on the half hour to make it 3-0 as Fulham continued to dominate possession with some neat passing.
Gera, one of four half-time substitutes, made an immediate impact by playing through Johnson, who coolly rounded the keeper to make it four just after the break.
Brentford began to exert more pressure on the away side, with Stockdale having to save from substitute Carl Cort, but Fulham always looked like adding more.
They soon found themselves five up when Gera's cross was met by Simon Davies at the back post, who beat Lee from six yards.
O'Connor was given a standing ovation as he was substituted two minutes before the end as Fulham played out the closing stages to seal a comfortable win.