Leeds went ahead in the 34th minute through Ethan Ampadu who bagged his first goal for the club by crashing home a finish from close range after Jaidon Anthony's free-kick was chested down into his path by Patrick Bamford.
The Whites then doubled their lead two minutes after the interval via a wonder-goal from Bamford who hooked home a brilliant first-time volley into the top corner from around 25 yards out after superb control with his back to goal via his chest.
Leeds were cruising into round four and there was still time for a third goal as Ampadu bagged his second goal of the game in the 90th minute by heading home a Dan James corner.
Graham Smyth, the YEP’s chief football writer, hands out the scores from Sunday’s clash at the Weston Homes Stadium against Posh.
1. Kristoffer Klaesson
6 - A couple of errant kicks and one second half spillage aside he did well at crosses and saved smartly with his feet in the second half. Little else to do. Photo: Joe Giddens
2. Jamie Shackleton
6 - The usual earnest shift, got himself up and down and offered runs down the right to give Leeds an outlet. Had real issues with Mason-Clark. Photo: Marc Atkins
3. Joe Rodon
9 - Imperious. Controlled things at the back, always got himself into the right place, tackled, headed and passed it really well. Organised the back four, too. Photo: Marc Atkins
4. Ethan Ampadu
9 - Some lovely passing, some strong defending and a first goal for Leeds, at long last. Claimed an assist on the Bamford wondergoal, too. Photo: Marc Atkins
5. Junior Firpo
6 - Went in for tackles and didn't get the ball a couple of times, which allowed Posh in. Some good work going forward in possession. Photo: Marc Atkins
6. Ilia Gruev
7 - Started really well, faded a little as Kyprianou took over for a spell and then grew back into it in the second half. Good at nipping in and timing his tackles. Photo: Marc Atkins