The Bantams chalked up only a second win in ten outings thanks to second half goals from Jacob Butterfield, Eoin Doyle and Lewis O’Brien.
Posh replied with a controversial late penalty by Marcus Maddison but there could be no doubting that the better team won.
Bowyer had clearly urged his players to keep the ball on the floor more than had been the case under predecessor David Hopkin.
The new Bradford chief also moved Butterfield into a more forward position and the on loan midfielder from Derby County delivered a fine display.
He came closest to breaking the deadlock during the first half with a free-kick that struck the crossbar.
Otherwise, neither goalkeeper had a save to make in those opening 45 minutes despite plenty of endeavour from the two teams.
Bradford then seized the initiative after half-time. Butterfield put Bowyer’s men in front on 70 minutes, his drilled effort from 20 yards beating Conor O’Malley at his near post.
Doyle doubled that advantage six minutes from time following neat play from David Ball, who had been released by a sublime piece of vision from new captain Hope Akpan.
Lewis O’Brien added a third two minutes later after being set up by Doyle before referee Matthew Donohue awarded Posh a late penalty despite Paul Caddis clearly getting the ball in a challenge on Maddison.
Richard O’Donnell was unable to keep out Maddison’s spotkick but it could not spoil the afternoon for a City side who now sit four points adrift of safety with ten games remaining.