The defeat means Jim Gannon's side are still without an away win this season.
When the two sides met at the end of December, Cardiff threw away a four-goal lead and were forced to settle for a 4-4 draw at London Road but there was to be no repeat of those heroics.
Stephen McPhail captained Cardiff in only his second game back since recovering from cancer treatment. City started positively with forward duo Michael Chopra and Jay Bothroyd causing the visitors problems in the early stages.
Former Newcastle striker Chopra headed the ball down for Bothroyd, but his strike partner hit a left-footed shot against a post. The pair linked up well again soon after but Chopra fired his effort wide of the right-hand post.
Cardiff came even closer to breaking the deadlock after 16 minutes but Joe Lewis produced a fine save to tip Peter Whittingham's free-kick over the bar for a corner.
But the Bluebirds were dealt a blow just five minutes later when Darcy Blake was forced off with an injury to be replaced by youngster Aaron Wildig, who had scored their only goal at Newcastle.
Peterborough would have been disappointed not to open the scoring when George Boyd headed wide from Ryan Bennett's cross.
And that miss proved costly as Jones' men broke the deadlock after half an hour. Whittingham's cross found Bothroyd, who headed the ball down for Burke to fire home from six yards.
The midfielder should have doubled his tally soon after but he was unable to keep his header down as it sailed over the bar.
Cardiff continued to dominate in the first half but failed to convert another chance when Whittingham shot wide of the right post.
Peterborough tried to find a way back into the game in the second half as Aaron Mclean hit a weak shot over the bar, before Posh had to rely on their goalkeeper to keep them in the game.
Whittingham's right-footed effort was well parried by Lewis before Burke drilled the rebound wide of the left-hand post.
But Cardiff were not to be denied a second goal as Whittingham floated in a free-kick which was flicked on by Bothroyd, who later went off with an injury, for Gerrard to poke beyond Lewis 12 minutes from time.