Darren Ferguson's men are into the area final of the Johnstone's Paint Trophy after a dogged display at Rodney Parade with goals from Kgosi Ntlhe, Grant McCann and Nathaniel Mendez-Laing securing a 3-0 victory at Newport County.
After a quiet opening, Posh got their noses in front just before the quarter-hour and it came from an unusual source. Left-back Kgosi NTLHE burst forward, and fired a low, skiddy effort that goalkeeper Stephens failed to keep out.
On 19 minutes, Connor Washington should have done better with a close-range effort after a glorious Pipe delivery from the right as Newport responded well to falling behind.
A curling free-kick from Lee Tomlin was pushed aside by Stephens on 25 minutes. A minute later, Jeffers headed over after a cross from Swanson on the left.
Posh were forced into a change on 37 minutes as Little limped out of the action, Nathaniel Knight-Percival his replacement with Bostwick moving across to right-back.
On the stroke of half-time, Posh nearly caught the home side on the counter-attack, but Swanson's ball lacked pace and Jeffers eventual shot was saved. In stoppage time, Olejnik produced a stunning one-handed stop to deny a dipping volley from Robbie Willmott before official Mr Kettle brought the first half to a close.
Newport made a double change at the break with former Posh front man Danny Crow among those introduced. Jolley fired over on the half-volley on 53 minutes as Newport made a bright start to the second period.
Jolley was then denied by Olejnik as his left-foot curler was pushed behind by the Posh shot-stopper. Jeffers saw a low shot cleared from danger after good work from Assombalonga in a tight spot close to the touchline.
Willmott tested Olejnik from 20-yards with the Posh shot-stopper doing well to gather the ball into his body. Washington fired low but wide of the near post on 80 minutes as the hosts continued to press for the equaliser.
Ntlhe was close to a second goal on 88 minutes after racing down the left, but his low shot was pushed behind for a corner kick. Tomlin was superbly denied by Pidgeley on 89 minutes, but a minute later, Posh made it 2-0 as McCANN found the bottom corner with a left-footed drive from 20-yards.
Deep into stoppage time, Posh wrapped it up as Tomlin fed substitute MENDEZ-LAING who rounded the goalkeeper and fired into an empty net from an acute angle.
Final Score: Newport County 0-3 Posh
Newport: Stephens (sub Pidgeley 62min), Pipe, Hughes (sub Crow 46min), Chapman, Willmott, Washington, Sandell, Naylor (sub Flynn 46min), Oshilaja, Worley, Jolley. Unused subs: Minshull, Barker.
Posh: Olejnik, Little (sub Knight-Percival 37min), Ntlhe, Brisley, Bostwick, McCann, Anderson, Swanson (sub Ferdinand 63min), Tomlin, Jeffers (sub Mendez-Laing 71min), Assombalonga. Unused subs: Day, Payne.
Attendance: 1,755 (165 Posh fans)