Bryan Mbeumo's blistering volley midway through the first half was enough to leapfrog the Cottagers and lift the Bees to fourth in the Championship.
The hosts outplayed their rivals for long spells, hitting the woodwork three times and forcing keeper Marek Rodak into a string of saves. In the end, the single goal was enough to consign Fulham to their third defeat in a row.
The goal came in the 22nd minute after a lightning counter attack when Ollie Watkins held the ball up and slipped it through to Said Benrahma, whose first-time cross was smashed home at the far post by the French Under-21 winger.
It was no more than the Bees deserved for a powerful high-tempo performance that left Scott Parker's side looking bewildered for long spells of the first half.
The visitors started brightly though, Neeskens Kebano cutting in from the left to fire off a low drive that span to safety off the outside of the upright.
Stefan Johansen was next to try a range finder, but his low bobbling effort from the edge of the box flew just past the other post.
Brentford were clinical on the break, and Benrahma raced clear to feed Mathias Jensen but the midfielder's stinging drive was well saved low to his right by Rodak.
The hosts grew in confidence after the opener and should have stretched their lead eight minutes with another piece of text book counter attacking.
Mbeumo was the provider this time, his early cross finding Watkins in full flight only for the striker to hit the post on the stretch before Josh Dasilva fired the rebound inches wide.
Brentford could count themselves unlucky not to have gone in with more than the one-goal cushion when the woodwork came to Fulham's rescue again in first half injury time.
Jensen's corner was met at the near post by skipper Pontus Jansson, whose downward glancing header bounced to safety off the angle.
Dasilva fired narrowly wide on 53 minutes before forcing Rodak into a low save as the Bees attacked with intent and tempo.
Jensen was the next to test the woodwork, his clever shot from the edge of the area squirming through Rodak's hands and onto the post before rolling along the line.
Dasilva, Watkins and then Jensen all tested the overworked Rodak's concentration with a flurry of efforts as the visitors' goalkeeper led a charmed life.
The closest Fulham came to an effort on goal came in the 87th minute when Anthony Knockaert fired over the bar as Fulham threw men forward in a desperate search for a leveller.
They managed just two efforts on target and Brentford's only regret was that they did not push the goal difference total up.
But the more they pressed the more Brentford broke at speed with real intent, with Benrahma and Mbeumo working well around the fulcrum of Watkins.