Steve Cotterill's men had seen their lead at the top of the table cut to just one point after back-to-back 1-0 losses to Swindon Town and Preston North End, but they were back in form at London Road on Friday.
An away win rarely looked in doubt as goals from Luke Freeman and Aaron Wilbraham gave City a 2-0 lead after just 16 minutes.
Freeman then doubled his tally to secure a comfortable three points just after the hour, with Peterborough now winless in five League One games.
Friday's other League One match saw fifth play sixth as Sheffield United hosted Notts County.
County were on course for a valuable victory when Mike Edwards headed them ahead after 31 minutes.
However, United's attacking persistence eventually paid off, and they snatched a point when Jamie Murphy nodded past the helpless Roy Carroll from close range 14 minutes from time.
Elsewhere in the Football League on Friday, Exeter City claimed a thrilling 3-2 win at Accrington Stanley in League Two.
Liam Sercombe gave Exeter the lead in the third minute of first-half stoppage time, and the visitors' advantage was doubled just four minutes after the restart through Tom Nicholls.
John O'Sullivan pulled one back for Accrington in the 65th minute, before Matt Grimes swiftly restored Exeter's two-goal cushion.
Accrington enjoyed some late pressure after Shay McCartan's 73rd-minute goal inspired a desperate search for an equaliser, but Exeter held on for all three points.
