Willian scored Chelsea's third early in the second period, but John Terry was then sent off for the home side in the 67th minute and four minutes later, Tom Nichols was on the scoresheet for the visitors.
Pedro added his second in the 75th minute, however, as Chelsea comfortably advanced into the next round.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
CHELSEA: Begovic; Zouma, Terry, Cahill, Ivanovic; Fabregas, Chalobah, Loftus-Cheek; Pedro, Batshuayi, Willian
POSH: McGee; Smith, Bostwick, Tafazolli, Hughes; Edwards, Forrester, Nichols, Maddison; Angol, Lopes
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