The hosts claimed a 3-1 victory over Forest Green Rovers to reach the second round, while the Posh held their nerve to beat Swindon Town on penalties.
Match preview
Since losing to Sheffield Wednesday in March, Portsmouth have embarked on an impressive 18-game unbeaten run in all competitions.
While John Mousinho will be pleased with his side's consistency, he will be frustrated by the fact their last two league games have finished goalless.
However, those two goalless affairs have helped Pompey record four consecutive clean sheets in League One, and they will look to produce another strong defensive display in Tuesday's meeting with Peterborough.
Portsmouth have been eliminated in the second round of the EFL Cup in two of the last three seasons, including last term when they were beaten 3-2 by Newport County.
If they can progress to the next stage on Tuesday, it would represent the first time they have reached the third round since the 2019-20 season.
Meanwhile, Peterborough began the season with a positive run of results, recording three successive league wins, while beating Swindon on penalties to move into the second round of the EFL Cup.
However, Darren Ferguson's side were stopped in their tracks by a 1-0 defeat to Northampton, and they were unable to bounce back in Saturday's home meeting with Derby County.
While Jonson Clarke-Harris and Kwame Poku got on the scoresheet, a Martyn Waghorn hat-trick and an Eiran Cashin strike condemned Peterborough to a 4-2 defeat against the Rams.
The Posh will be hoping to return to winning ways in their first of two trips to Fratton Park in a matter of days, with the two sides set to meet again in Saturday's league fixture.
Peterborough are competing in the second round of the EFL Cup for the second straight season, and they are looking to reach the third round for the first time since the 2013-14 season.
Portsmouth EFL Cup form:
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Portsmouth form (all competitions):
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Peterborough United EFL Cup form:
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Peterborough United form (all competitions):
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Team News
Portsmouth are unable to call upon the services of Tom Lowery and Kusini Yengi, with the pair ruled out with injury issues.
Zach Swanson is expected to replace the suspended Joe Rafferty, who was shown a straight red card in Saturday's goalless draw against Stevenage.
Mousinho could be tempted to make a number of other changes to his side, with Ryan Schofield, Sean Raggett, Terry Devlin, Alex Robertson and Paddy Lane all in contention to start.
As for the visitors, midfielder Jeando Fuchs has been ruled out until December with a thigh problem, while a hip issue will prevent goalkeeper Will Blackmore from being involved.
After featuring as a substitute in each of the last three matches, Ricky Jade-Jones could be brought into the side for the midweek cup tie.
Clarke-Harris is currently being linked with a move away, but as it stands, the striker is expected to start against Portsmouth.
Portsmouth possible starting lineup:
Schofield; Swanson, Raggett, Shaughnessy, Ogilvie; Pack, Devlin; Lane, Robertson, Kamara
Peterborough United possible starting lineup:
Bilokapic; Kioso, Edwards, Crichlow-Noble, Burrows; Kyprianou, Collins; Poku, Jade-Jones, Mason-Clark; Clarke-Harris