Pompey saw off Barnsley to reach the fifth round of the Emirates FA Cup for the first time in a decade.
They beat the Championship side 4-2 at Fratton Park and were dominant for much of the contest.
Ben Close and John Marquis both struck late in the first half to ensure the hosts had a commanding interval lead.
Christian Burgess then nodded home from a corner, while former Pompey striker Conor Chaplin grabbed a late consolation for the Tykes.