Pompey will host Wycombe Wanderers in the second round of the Johnstone’s Paint Trophy.
And the Fratton Park clash will be held in the week beginning October 8.
Pompey overcame Bournemouth on penalties in Tuesday’s first-round tie.
Draw: Northern Section: Shrewsbury Town v Crewe Alexandra; Rochdale v Bury; Morecambe v Preston North End; Walsall v Port Vale; Doncaster Rovers v Chesterfield; York City v Coventry City; Notts County v Sheffield United; Hartlepool United v Bradford City. Southern Section: POMPEY v Wycombe Wanderers; Cheltenham Town v Oxford United; Torquay United v Yeovil Town; Plymouth Argyle v Aldershot Town; Northampton Town v Colchester United; Leyton Orient v Barnet; Brentford v Crawley Town; Southend United v Dagenham & Redbridge