The Sky Bet League One hosts are unbeaten at home in the league this season and more than played their part in an entertaining cup tie, with the Gunners eventually running out 2-0 winners.
While the travelling fans sang about their 49 games unbeaten in the wake of Liverpool's 44-match streak ending at the weekend, adding to their record 13 FA Cup wins remains their only chance of silverware this season.
Sokratis was the next Arsenal defender to be left flummoxed, the Greece international operating at right-back and getting turned too easily by Marcus Harness as the hosts looked to take the game to their top-flight visitors.
Arsenal's somewhat slow start was not helped when Lucas Torreira was floored by a strong challenge from James Bolton which resulted in the midfielder being taken off on a stretcher to be replaced by Dani Ceballos.
The Gunners finally forced Alex Bass into action as Bukayo Saka burst forward down the left and shot low at the Pompey goalkeeper before Harness had a curling effort deflected behind at the other end.
Gareth Evans spurned the best chance of the game just before the half-hour mark, miscuing a header having steamed into the box to meet Steve Seddon's cross following a quick free-kick.
It was Arsenal's turn to bemoan a missed header as Gabriel Martinelli could only steer Reiss Nelson's flashed cross over from close-range as the first-half looked set to end goalless.
That changed in the fourth minute of added-on time as an Arsenal corner was cleared to Ceballos, who played in Nelson to cross for Sokratis to turn home with a fine volley.
Arsenal were much faster out of the traps for the second half and doubled their advantage soon after the restart, Nketiah finishing well from close-range following another Nelson centre.
England Under-21 international Nelson was enjoying himself and broke through to see a shot blocked behind before Saka had a strike tipped over with the visitors in complete control of proceedings.
They could not add to their lead, Andy Cannon coming closest as Portsmouth searched for a consolation at the other end in the closing stages.
With the strength of the opposition still left in the cup it is unlikely Arteta will be afforded the luxury of making sweeping changes next time out and, for Portsmouth and Jackett, focus can now shift back to their League One promotion bid.