Aleksandar Mitrovic netted twice to set a new Championship goalscoring record and take Fulham nine points clear at the top of the table.
The striker’s brace took his goal tally for the campaign to 33, eclipsing Ivan Toney’s 31 for Brentford last season.
He opened the scoring with a penalty after being fouled by Harrison Burrow.
And he doubled the lead with a lovely side-footed volley from Neeskens Kebano’s cross.
Jack Marriott scored an 89th-minute consolation goal for Peterborough.
Fulham: Rodak, Williams, Tosin, Ream, Robinson, Reed (Wilson 63), Seri, De Cordova-Reid (Onomaha 83), Carvalho, Kebano (Cavaleiro 63), Mitrovic.
Subs not used: Gazzaniga, Tete, Hector, Chalobah.