There were two changes in the Bluebirds line-up with Mark Kennedy and Burke replacing Adam Matthews and Ross McCormack, who were both on the bench.
Peterborough, without a victory away from their London Road home, were looking to win two in a row after defeating QPR 1-0 at the weekend.
A neat interchange between Michael Chopra and Jay Bothroyd in the fourth minute almost led to the opening goal but Bothroyd's curler beat Posh keeper Joe Lewis only to come back off the foot of the post.
Peter Whittingham fired in a free-kick from the right that Lewis had to tip over for a corner in the 17th minute but, although City had most of the possession, they were unable to create any clear goalscoring chances.
The Bluebirds were forced to make an early change with the injured Darcy Blake making way for Aaron Wildig midway through the half.
The breakthrough came on the half hour when Whittingham sent a cross to the far post. Bothroyd headed it back into the danger area where Burke controlled the ball before lashing into the net for his seventh goal of the season.
Six minutes later another Whittingham cross was headed over by Burke as City began to put the visitors under pressure but half-time came with no further goals.
Former City loanee Kerrea Gilbert came on for Craig Mackail-Smith at the start of the second half and two corners put the home side on the defensive as they failed to clear their lines.
Apart from a Whittingham shot that Lewis pushed behind, the Bluebirds seemed unable to keep hold of the ball and in the 76th minute George Boyd found himself in front of goal but scuffed his shot straight at David Marshall.
Stephen McPhail left the field shortly after to be replaced by Solomon Taiwo and City doubled their lead straight away in the 78th minute when Whittingham's free-kick was touched on and Gerrard poked it past Lewis.
Chopra struck the foot of the post with a snapshot in the closing minutes and the Bluebirds played out the five added minutes to record a deserved victory.