It was Warburton's fifth victory in a row since taking over as manager from Uwe Rosler and moves them three points clear of second-placed Wolves.
Adam Forshaw's penalty (16) was cancelled out by Jack Payne (33) but Posh were level for only three minutes before Sam Saunders restored Brentford's lead.
Forshaw missed a second penalty but it did not cost them and Clayton Donaldson added gloss to the scoreline with an injury-time third.
Wolves drew 1-1 with Tranmere in a game that was 10-a-side by half-time, Richard Stearman and James Wallace seeing red.
Ryan Lowe (34) put hosts Tranmere ahead but Dave Edwards (55) earned Wolves a point.
Third-placed Leyton Orient fell foul of the weather, with the matches at Stevenage and Swindon also being postponed because of waterlogged pitches.
Preston took advantage and closed to within one point of Orient with a 3-2 victory over Port Vale.
Preston looked to be coasting as a brace from Joe Garner (43, 62) either side of a Paul Gallagher strike (50) put them three up but goals from Gavin Tomlin (69) and Jordan Hugill (84) made for a nervy finish.
Coventry continued their climb up the table thanks to a 3-1 victory over Rotherham that featured a dramatic finish.
Joe Skarz put Rotherham ahead (34) but Craig Morgan was sent off for a foul in the box and Carl Baker (70) netted the penalty to level matters.
Franck Moussa (85) then gave the visitors the lead and Michael O'Connor missed a chance to level from the penalty spot in the 12th minute of injury-time before Baker grabbed Coventry's third.
The biggest winners of the day were Notts County, who defeated Bradford 3-0 with goals from Jamal Campbell-Ryce (32), Callum McGregor (88) and Jack Grealish (90) to climb off the bottom of the table.
Walsall are up to seventh, the Saddlers coming from behind to defeat Sheffield United 2-1.
Chris Porter (17) put the visitors ahead but Craig Westcarr (52) levelled from the spot and James Chambers scored the winner 10 minutes later.
Shrewsbury secured their second away victory of the season with a 2-1 win at Oldham.
Jon Taylor (23) put the Shrews ahead, Jonathan Grounds (35) equalised before Aaron Wildig scored the winner in the 62nd minute.
Down at the bottom, there was a big win for Crewe as they beat Carlisle 2-1.
Chuks Aneke (53) and Buomesca Tue Na Bangna (64) gave Alex the advantage and Carlisle could only manage a free-kick from Tom Lawrence (78) in response.
In the final game of the day, mid-table sides Milton Keynes Dons and Colchester drew 0-0.