Defender Bostwick blasted the only goal at London Road when arrowing home a low set-piece through a crowded penalty area and past visiting goalkeeper Carl Ikeme with 11 minutes remaining.
That was enough for Darren Ferguson's side to snap a run of five successive league defeats and collect a first win in seven games. It also sent leaders Wolves crashing to a first away loss of the campaign.
Posh were fortunate to survive an early penalty appeal when Mark Little appeared to handle Bakary Sako's cross and the same Wolves player was guilty of greed late in the opening period when firing into the side-netting after breezing past defender Kgosi Ntlhe.
Wolves' top scorer Leigh Griffiths and defender Danny Batth also fluffed good headed opportunities during the first half, but the visitors created little after the interval with only a classy Sako volley testing home keeper Bobby Olejnik.
The same could be said of out-of-form Posh, but they found a breakthrough when it mattered most to pocket three priceless points.