Kieran Agard struck from the spot - his 18th goals of the campaign - as the Millers stretched their unbeaten run to 13 games.
Nicky Adams was thwarted by Posh goalkeeper Bobby Olejnik when one-on-one, while Millers goalkeeper Adam Collin was also on top form to keep out the hosts.
“It was a big victory against a super team,” said Evans. “I think they are terrific in a number of areas.
“When you come to London Road, it’s a very tough place to come and we’re pleased to come away with three points.
“It’s one game at a time for us - our objective is to finish in that play-off place.”