Spanish midfielder Jota gave the Bees the lead on the stroke of half-time, finishing off a flowing five-man move with a crashing drive into the roof of the net.
And Alan McCormack sealed the points in the 76th minute with a rasping low drive that deflected off the foot of Giuseppe Bellusci and past despairing keeper Marco Silvestri.
The United stopper had kept his side in it with a string of superb saves as the Bees swarmed forward with purpose on the break.
United’s only real effort of merit came with five minutes remaining when Lewis Cook’s 25-yard grass-cutter licked just past the upright.
The Londoners looked purposeful from the start, Alex Pritchard forcing a smart low save from Silvestri at the foot of the post.
The keeper denied the hosts the opener on 22 minutes when he dived late to tip Alan Judge’s dipping, swerving free-kick over the wall into the path of Moses Odubajo only to block him at point blank range.
Brentford squandered a gilt-edged chance to break the deadlock midway through the half when Andre Gray was felled in the box by Jason Pearce who escaped with a yellow card.
Centre back James Tarkowski raised eyebrows when he stepped up to take the spot kick and duly skied it over the bar.
Former Leeds midfielder Jonathan Douglas almost headed his side in front minutes later but was again thwarted by the keeper.
The breakthrough came on the stroke of half time when Brentford’s slick passing carved open the visitors’ defence and found Jota who sidestepped Stephen Warnock to fire into the roof of the net.
Judge blazed over as Brentford started the second half as they ended the first, but at the other end Bees keeper David Button had to be alert to tip Pearce’s downward header to safety.
Mirco Antenucci fired wide with long-range efforts as Leeds staged a rally, but Brentford drew their sting and hit back with the pace of Odubajo a constant outlet.
The winger, a close season signing from Leyton Orient, fed Gray on the hour mark but his drive was saved by the legs of the wrong-footed Silvestri.
And the keeper was there again five minutes later when Odubajo slipped the shackles of Pearce to send a diving header goalward, going full length to palm it wide.
Both sides were struggling in the humidity but it was Brentford who made their possession count on 76 minutes.
Odubajo broke from half way and fed McCormack who raced clear of a leggy Leeds rearguard, bided his time and smashed a drive home from 12 yards.
That took the fight out of Milanic’s side and Brentford surged forward in search of more as they won almost every 50-50 battle in the middle of the park.
Leeds looked broken in a game that could easily have ended in a 6-2 scoreline such was the level of defending.