The Bees continue to breath-down the necks of the division's pace-setters, despite the departure of manager Uwe Rosler to Wigan earlier this month.
And it was the first-half goals from Adam Forshaw, a penalty, and Marcello Trotta that did the bulk of the damage for Warburton's men, with Sam Saunders adding a third after the break. .
Preston looked lively on the break but it was Brentford that went ahead from the penalty spot in the 23rd minute.
Clayton Donaldson latched onto a long ball and goalkeeper Declan Rudd raced out from the Lilywhites' goal bringing the striker down. Forshaw coolly dispatched the spot-kick and then set up the Bees' second goal shortly afterwards.
A slick passing move after 26 minutes allowed Forshaw a shot on goal that was parried by Rudd but the former Everton player hooked the ball back to Trotta who blasted home.
Preston were rewarded with a penalty after the break when Jake Bidwell was adjudged to have pushed Joel Garner inside the box. David Button saved the spot kick, diving to his right.
Kevin Davies could have scored moments later but he sent his free header across the face of the goal and wide.
Substitute Saunders killed the game off in the 73rd minute to extend Brentford's unbeaten run and end the Preston fightback.