Adam Forshaw's penalty, a classy Sam Saunders strike and a last-gasp Clayton Donaldson clincher secured a fifth successive victory since Warburton succeeded Uwe Rosler at the Bees' helm and sent faltering Posh to a third straight defeat.
Forshaw broke the deadlock in the 16th minute courtesy of his spot kick after Posh goalkeeper Robert Olejnik had dashed from his line only to take down Saunders.
Donaldson steered a golden chance to double the visitors' lead against a post before Posh levelled in spectacular style when Jack Payne's dipping 25-yard drive flew past Bees' goalkeeper David Button and in off the underside of the crossbar.
But parity was short-lived as Saunders coolly restored the Brentford advantage when guiding a fine low shot past Olejnik from 20 yards just three minutes later.
Forshaw could even afford to see another penalty, awarded after Payne had pulled down Donaldson, saved early in the second half before Donaldson secured Brentford's 12th win in 13 matches in time added on when tapping in Stuart Dallas's delivery.