He threw on David Clarkson just after the hour and the Scottish frontman soon provided the only goal of the game when being left unattended to glance home compatriot Paul Hartley's 71st-minute corner.
Clarkson later planted another excellent headed chance over the crossbar, but one goal proved to be enough to extend Millen's unbeaten record in temporary control to three matches.
Millen said: "I felt we were well worth the win in a game in which I always thought the first goal would be crucial.
"David has had a frustrating time since he came to the club, but he is an excellent finisher and he took his chance well.
"I'm obviously very happy with the way things have gone since I took charge and I'll be sitting down with the chairman this week to see where we go from here.
"I feel I have the experience and knowledge required for a managerial job at this level - and I absolutely love working at Bristol City.
"The players have shown they are performing for me and while the fans would probably like a big name to come in, hopefully they can see the results we are getting."
City always looked the likelier side throughout a generally poor spectacle.
Posh goalkeeper Joe Lewis kept out long-range efforts from Bradley Orr and Liam Fontaine in the opening 15 minutes before also denying Nicky Maynard.
It took rock-bottom Posh an hour to muster a noteworthy effort on goal as Exodus Geohaghon tested City goalkeeper Dean Gerken twice in quick succession. Gerken then had to react smartly to tip a Craig Mackail-Smith cross onto his own crossbar before City struck the killer blow at the other end.
Posh did press for an equaliser in the closing stages and even when Gerken had been beaten by a Lee Frecklington shot, defender Liam Fontaine was on hand to clear.
And while City chief Millen has made no secret of his desire to keep hold of the City job, Posh manager Jim Gannon has snubbed the chance to stay at London Road beyond the end of this season.
After seeing his side go down to a fourth straight defeat, he said: "There was nothing in a game of little quality and it was very disappointing to concede in the way we did from a set-piece.
"We spent hours studying videos and reports of Bristol City in those situations to try and ensure that didn't happen.
"The majority of players worked hard for the cause and looked motivated, but we ran out of ideas in the end."