Pompey performed nicely in the first half at Fratton Park however trailed to Sokratis Papastathopoulos’ volley from Reiss Nelson’s cross just before the break.
Eddie Nketiah bundled home from shut range to wrap up the victory six minutes after the restart.
Pompey’s only shot on target came in the 2nd half, with substitute Ronan Curtis’ effort saved.
The other fifth-round ties are on Tuesday, Wednesday and Thursday. The quarter-final draw on Wednesday after Sheffield Wednesday v Manchester City.
Arsenal came into this game on the returned of their shock Europa League exit to Olympiakos on Thursday.
Manager Mikel Arteta – slightly surprisingly – made nine changes, with a number of fringe players starting, and defender Pablo Mari making his debut, despite this being their only hope of silverware. They are eight points off fourth-placed Chelsea in the Premier League.
They lost Lucas Torreira to injury in the first half, the midfielder taken off on a stretcher after a tough but fair sliding tackle by James Bolton.
That was their only poor from the game at Fratton Park though.
Bukayo Saka – one of the two to maintain their place from Thursday’s defeat – forced a save and Gabriel Martinelli headed over the bar.
Sokratis opened the scoring with a high-quality volley from Nelson’s right-wing cross.
And Nketiah scored his third goal since returning from a loan spell at Leeds when he managed another Nelson pass before rifling into the roof of the net from close range.
From that point on Arsenal appeared cozy – and prolong their unbeaten run against Portsmouth to 22 games. They have not lost to Pompey since 1958.