Posh keep piling up the points in their surge towards League One but found Bury tough opponents in a contest decided just before the hour when Keates jumped at the far post to send a downward header past a helpless Darren Randolph.
Unlike most London Road visitors whose ambition rarely gets beyond trying to stifle the home frontline, Bury attacked with creditable gusto and had the two best chances of the opening half.
Adam Rooney lifted a shot high over the bar from 12 yards after a Brian Barry-Murphy corner was only partially cleared and Lewis stretched impressively to turn over a rising 25-yard effort from Shakers skipper Paul Scott.
Posh's best opening before the break fell to Charlie Lee who blazed wide and afterwards Craig Mackail-Smith grazed a Bury post and Aaron Maclean was just off the mark with a spectacular scissors kick.
Lewis, a £400,000 January capture from Norwich City, almost replicated his first-half heroics, this time palming away a blistering drive from Bury's former York frontman Andy Bishop.
Bury looked set to level six minutes after Keates struck with Nicky Adams bursting in from the left. Once again Lewis was equal to the occasion and after he parried the shot, Claude Gnapka managed to clear under pressure from Bishop.
Lewis has now kept clean sheets in his last five outings, but even he was relieved to see a late well-struck free-kick from Bury dangerman Bishop curl just wide of the left-hand upright.