First half goals from Romaine Sawyers and Lasse Vibe were enough to send United away empty handed as the Bees turned on the style.
Sawyers gave the home side the lead on 18 minutes when he smashed home from the edge of the box after Rob Green could only parry Sergi Canos' angled drive from the left to safety.
And Canos was involved for the second just after the half hour when his low drilled shot from the right was palmed into the path of Vibe, who toe-poked home for his 13th of the season.
It was a first half masterclass from Brentford, who played some scintillating football and restricted Leeds to just one clear-cut chance in the first 45 minutes.
That fell to Luke Ayling on the half hour - but his volleyed effort flew well over the bar after the unmarked Kyle Bartley's far post header was blocked.
Brentford could have gone in at the break four goals to the good, Vibe dinking an effort from a sublime Sawyers through-ball just past the far post two minutes later.
And Canos should have got on the scoresheet with 13 minutes gone, but blazed his first-time effort from Josh Clarke's low drilled cross from the byline well over.
Before the break United struggled to get anywhere near the hosts, whose fluent football left them chasing shadows.
They emerged stronger after the break and Modou Barrow forced a smart low save from Daniel Bentley at the foot of his post 10 minutes after the restart.
Pontus Jansson also went close with a far post header which was blocked, but Brentford looked dangerous on the break as the game entered a scrappy phase.
Rob Green tipped Jota's free kick over the bar midway through the half as Leeds pressed forward and left gaps as they went in search of a way back into the game.
Brentford almost stretched their lead on 77 minutes when Vibe raced onto a precise Sawyers through-ball, only to see his effort blocked by Green - who got up quickly to clear the onrushing Florian Jozefzoon's first-time effort off the line.
United had little answer to the midfield promptings of Ryan Woods and man-of-the-match Sawyers, who pulled the creative strings in an entertaining win.
Vibe almost put the icing on the cake at the end but Green was equal to his angled drive on the counter and Sawyers' piledriver from the rebound was blocked for a corner.
Leeds striker Chris Wood was well marshalled throughout by Harlee Dean as Brentford clocked up their seventh win out of eight night matches at Griffin Park this season.