City were unchanged from the team that beat Barnsley 5-3 in midweek while Posh made three changes with Scott Griffiths replacing the injured Mark Little and Nathan Koranteng and Josh Simpson replacing Reuben Reid and Sergio Torres.
The Robins had the best of the early stages and Bradley Orr's long-range shot brought a save from Joe Lewis.
From the resulting corner Liam Fontaine had a good chance but he put his header from six yards wide of the post.
Peterborough were then forced into an early substitution as Chris Whelpdale went off injured to be replaced by Kerrea Gilbert.
City's early dominance continued and Lewis was forced into a double save as he blocked Fontaine's effort and then scooped up the rebound from Danny Haynes.
Nicky Maynard, who was looking for his fourth goal in three games, then tested Lewis from distance but the keeper was equal to it before Jamal Campbell-Ryce dragged a shot wide.
The visitors continued to dominate possession but they struggled to convert their control into clear-cut chances and Orr saw a speculative shot go wide.
Millen's men began the second half in similar fashion to the first and Maynard put a shot from 12 yards wide.
Cole Skuse then put a shot wide before the home side had their first meaningful chance of the afternoon.
Lee Frecklington swung in a corner which was met by the head of Charlie Lee but Louis Carey did a good job to block and prevent Posh taking the lead.
Jim Gannon's men were beginning to find their feet and following a series of corners Exodus Geohaghon had a header form six yards saved by Dean Gerken.
Danny Haynes was then replaced by David Clarkson in the 61st minute and ten minutes later the substitute gave his side the lead.
Paul Hartley delivered the corner and Clarkson rose highest to head home and give the Robins the goal that their superiority had merited.
And he very nearly doubled the lead when the unlikely figure of centre-half Christian Ribeiro charged down the right and provided a cross which Clarkson headed inches over the bar.
Geohaghon then saw another header go wide before Peterborough had their best chance of the afternoon with two minutes remaining.
Lima Fontaine was called upon to make a double block as first he cleared Frecklington's shot off the line and then, when the former Lincoln man headed his own rebound goalwards, Fontaine was again on hand to make the clearance.