The home side lost club captain John Terry to a red card in the second period, but held off the threat of a late Peterborough comeback to comfortably advance into the next round of the competition.
Kurt Zouma came in for his first start for 11 months following a long injury layoff, while Terry returned to captain the team. Elsewhere, Nathaniel Chalobah and Ruben Loftus-Cheek were given midfield spots, while Michy Batshuayi was given a rare chance to impress in the absence of Diego Costa.
As for Peterborough, head coach Grant McCann has made just three changes from the side that drew 1-1 with Scunthorpe United in the league last time out.
It was the same back five, but there was one change in midfield as the much-coveted 18-year-old Leo Da Silva Lopes replaced Martin Samuelsen. The front two were also altered as Tom Nichols and Lee Angol were selected over Junior Morias and Paul Taylor.
Chelsea's first half-chance of the match arrived in the sixth minute when Cahill met a near-post corner, but Posh goalkeeper Luke McGee was on hand to make a really smart save.
The chances continued to arrive inside the opening 12 minutes and Terry was next to come close for Chelsea after meeting another Willian corner, but McGee made a smart reaction save to keep the score goalless, before Ryan Tafazolli headed wide of the home side's post down the other end.
Eventually Chelsea made the breakthrough in the 18th minute when Pedro curled one into the top corner after a long-range strike from Chalobah had been palmed into the Spaniard's path by Posh goalkeeper McGee.
McGee made a smart save to prevent Batshuayi from making it 2-0 in the 30th minute of action, before Pedro quite incredibly smashed the crossbar from close range after the impressive Loftus-Cheek had put one on a plate for the former Barcelona attacker.
Chelsea did double their lead in the latter stages of the first period, however, when Loftus-Cheek found Batshuayi with a clever flick and the Belgian international smashed one into the bottom corner as Peterborough conceded a second in the 44th minute.
Loftus-Cheek should have sent Chelsea three goals ahead early in the second period when he was released by Fabregas, but the midfielder just placed his effort wide of the far post.
Chelsea were dominant though and made it 3-0 in the 52nd minute when Willian moved inside his full-back before picking out the bottom corner with an expert finish to end Peterborough's hopes of a comeback.
Chalobah missed a super chance to make it four in the 54th minute, before both managers made changes ahead of the final 30 minutes, which seemed purely academic due to the nature of the scoreline and Chelsea's domination.
Peterborough had a brilliant opportunity to get on the scoresheet 25 minutes from time when Branislav Ivanovic fouled Angol just outside the Chelsea box, but Michael Bostwick's effort was straight into the wall.
It was not all positive for the home side, however, as Terry picked up a straight red card in the 67th minute following a last-man challenge on Angol, although the resulting free kick was wasted by Taylor.
Peterborough had one back in the 71st minute, however, when Angol's effort fell to Nichols and the striker was quick to react as he turned the ball past Begovic to potentially set up a grandstand finish in London.
Chelsea made sure of a comfortable final 15 minutes though when Pedro curled his second into the bottom corner, and that proved to be the end of the scoring in the English capital as Conte's side breezed into the fourth round of the FA Cup once again.
Next up for Premier League leaders Chelsea is a trip to the champions Leicester City in the league next weekend, while Peterborough will continue their League One campaign with a trip to Bury.