It was end-to-end in the early proceedings, with chances for Gary Cahill and Lee Angol, but goals from Pedro and Michy Batshuayi saw the tie turn in the hosts favour.
Willian saw off the tie early in the second period, before the hosts were reduced to ten men with John Terry's dismissal. Tom Nichols got one back for the Posh, but Pedro rounded off a easy afternoon at Stamford Bridge.
The FA Cup has been Chelsea's favourite cup competition for the last decade, winning four in the last ten years.
However they were tested by lower league opponents in the opening exchanges. Antonio Conte's side had the first chance seven minutes in, when Cahill flicked on Willian's corner but Luke McGee did well to tip it around the post.
However two minutes later it was the visitors that almost took a shock lead. Marcus Maddison sent the ball forward looking for the touch of Angol, but Asmir Begovic to snuff out any danger.
Normal service resumed
Grant McCann's side looked like that they could cause problems to their top-flight opponents, but it wasn't long before Chelsea found themselves ahead.
It was an excellent team effort from the Blues, Willian wriggles his way into box playing it off to Cesc Fabregas. Ruben Loftus-Cheek had his effort blocked before falling back to Nathaniel Chalobah, his effort was brilliantly saved by McGee but the rebound found Pedro who curled it into the top corner.
The former Barcelona man should have made it two ten minutes before the break. McGee did brilliantly to block Loftus-Cheek's effort who decided to pass it to Pedro at the second attempt. He had the goal at his mercy but managed to clatter it off the crossbar.
Batshuayi had been waiting for his opportunity in the Conte's starting XI, and he made his talent known as he added the second just before the break.
It was simple enough for the Blues as Branislav Ivanovic played it in from right, his cross was flicked on by Loftus-Cheek and the Belgian forward was there to slide it home.
Making sure of it
Chelsea continued to turn the screw as the second half got underway, and it should have been three four minutes after a restart.
Fabregas managed to steal possession before sending Batshuayi through on goal, he laid it off to Loftus-Cheek and with the goal gaping as McGee flys off his line but he flashed it wide.
It wasn't long until they added their third, and Pedro was involved once again. He powered down the wing before picking out Willian in the area, the Brazilian did well as he took a few touches before curling the effort past McGee.
Little bit of magic
Conte's side were cruising from that point onwards, but managed to find themselves down to ten men in the 66th minute.
It was rare appearance for skipper Terry, but for a man of his experience his tackle was poor on Angol and was given his marching orders.
Not long after the traveling contingent managed to get what would prove to be a consolation for McCann's side. Michael Smith got down the right flank before a cross was flicked into the path of Nichols, and he turned it home at the back post.
Cruising on through
Despite that goal it was still all Chelsea, and they managed to add a fourth with 15 minutes to play. It was brilliant give and go from Pedro and Batshuayi with the Belgian laying it off, and he did brilliantly to take aim and curl it home.