Max Booth’s brace either side of half-time meant Neil Redfearn’s side left Cambridgeshire empty handed.
Will Brook was kept busy in the Farsley goal in the opening stages as he made saves to deny Michael Gash, Will Van Lier, Bayley McCann and Booth as the hosts dominated the opening 10 minutes.
Sports then took the lead on 32 minutes as Booth got on the end of Ben Lomax’s cross to head home the opener.
Peterborough doubled their lead on the 65th minute mark as Booth won a penalty after being Brough down in the area and he duly converted from 12 yards.
Brook continued to earn his corn in the Farsley goal, twice denying Booth his hat-trick before keeping Ryan Fryatt’s header out.