Dougie Freedman's side are unbeaten in five games since Dawson arrived on loan from West Brom in the January transfer window.
The central defender scored twice in Saturday's 4-1 thrashing of Hull and grabbed the only goal on Tuesday night with a firm header from Jay Spearing's fifth-minute corner.
Bolton proved far superior to their opponents in the first half, but lost their way after the interval and were grateful for Peterborough's lack of penetration.
Having been three up inside eight minutes against Hull, Wanderers wasted little time in taking the lead on this occasion.
Spearing's opening corner from the left failed to beat the first man, but his second delivery was much more inviting and Dawson got a run on his marker to head home.
Grant McCann shot tamely at Adam Bogdan as Peterborough looked to respond, but Bolton remained firmly in the ascendancy with two presentable chances falling to Lee Chung-yong.
The South Korean midfielder failed to keep a left-footed effort down, after Darren Pratley's low cross had come through a crowd of bodies, and then forced Bobby Olejnik into a fine diving save following a swift break.
Bolton soon went close again, with Olejnik denying David Ngog from a corner and Marvin Sordell heading wide seconds later.
Yet Peterborough, for whom Davide Petrucci limped off to be replaced by Jack Payne, threatened prior to the break as some casual home defending culminated in Nathaniel Mendez-Laing dragging a shot wide from close range.
A scrappy start to the second period prompted Wanderers to introduce Craig Davies for Sordell in the 58th minute.
Bolton briefly sparked back into life and both David Ngog and Marcos Alonso saw efforts fly narrowly past Olejnik's left-hand post either side of the former making way for Kevin Davies.
Despite enjoying more and more possession as the final whistle approached, Peterborough could find no way through and it was Craig Davies who came closest to scoring late on with a scuffed strike on the turn that Olejnik parried away.