Despite having to thumb a lift to London Road with a supporters' transport after their team coach broke down, Chester certainly hadn't lost their way on the pitch, although Posh were far from their best in a scrappy first half.
Aaron McLean missed a great second minute chance to settle nerves following an opening created by George Boyd and Jamie Day.
It was the 37th minute before McLean troubled City's John Danby again, but his spectacular overhead kick that was straight at the keeper. In between, only midfielder Charlie Lee seemed willing to have a crack.
Chester found it hard to provide any sort of service for big frontman John Murphy although Posh's Joe Lewis did well to advance and take a swirling cross off the head of Glenn Rule.
Posh forced the pace after the break but were no better in front of goal.
Scott Rendell released Boyd only to fluff a shot from six yards when the cross came through and the on-loan Cambridge front man again failed to hit the target with a header from a cracking centre by Chris Whelpdale.
Rendell was also denied by the woodwork before Posh finally broke the deadlock, with Rendell flicking the ball on for McLean's 71st minute cross to be met by Keates, who leapt to head past Danby for his fourth goal of the season.
In the last couple of minutes Chester's Tony Dunning was sent off for a second bookable offence after squaring up to Keates yet, in added time, they might have saved a point but for Shaun Kelly blazing wide.