Within a minute JWilliams, a veteran of 16 clubs in a career including top level experience with Coventry and Stoke, fired into the side netting. Driven on by player manager Gary Owers from midfield, Bath's neat football stretched the home defence and it was more than half an hour before Posh began to assert themselves.
The pace of David Farrell caused most of the problems, including a cross by the lively winger from which Andy Clarke had an effort saved at close range by Steve Perrin.
The Bath goalkeeper, on loan from Forest Green, stood no chance when Willock opened the scoring with a low 36th minute shot after Andre Boucaud pulled back a perfectly placed cross from the right-hand by-line.
Perrin's finger tips prevented Adam Newton scoring to celebrate his 24th birthday just before Willock headed his second on 41 minutes. Bath furiously contested the goal with Perrin earning himself a caution after protesting that Willock was offside as he finished off good work by Andy Legg and Sagi Burton.
With nothing to lose, Bath put pressure on Posh in the closing stages. Michael Sykes fired straight at Mark Tyler and the home goalkeeper also saw efforts from Williams and defender Graham Power go wide.