Third-tier Pompey had not beaten Arsenal since a 5-4 league victory in 1958, but they caused the Gunners plenty of problems before the deadlock was broken just before the break.
Reiss Nelson's cross was met with a sweetly-timed volley inside the area from Greece international Sokratis who put the Gunners ahead in first-half stoppage time.
The goal seemed to give Arsenal an injection of confidence and Nketiah made it 2-0 six minutes after the break, controlling a cross at pace before bundling the ball home from close range.
Portsmouth, roared on by their passionate fans, defended well but lacked spark in attack as Arsenal, the FA Cup's most successful side with 13 titles, held on for a comfortable win.
Arsenal's win was soured by Lucas Torreira suffering a leg injury, with the midfielder being substituted at halftime and seen leaving the stadium afterward on crutches.
"It's a difficult place to come but I have faith in these kids. They always respond and I always knew they would do that," Arsenal manager Mikel Arteta said after the match. "They have to learn from the difficult moments and manage them but they have the talent and desire and look how hard they work.
"I'm really enjoying working with this group of players,. It's a process. I know everything has to be today or yesterday but in football it doesn't happen like this. I'm seeing a lot of things I'm happy with but there is a lot of room to improve.
On Torreira's injury, Arteta said: "Lucas was very sore and is in a brace. He will be assessed in a few days and then we will know more."
Scorer Nketiah revealed that Arteta had urged his players to increase the tempo and intensity in the second period in order to put the result beyond doubt.
"The goals came at the right time, we knew we were in for a hard game, knew the first goal would settle things," Nketiah said after the game.
"Then we kept pressing and going for the third. It was a great performance from the team.
"The manager said to keep going and up our intensity in the second half. We played quicker, gaps appeared and that's when we played out best football."
The rest of the fifth-round ties are being played in midweek due to the short winter break in the Premier League, with the draw for the quarterfinals taking place on Wednesday when holders Manchester City visit Sheffield Wednesday.
For Portsmouth, who sit in third place in the League One table, the focus now turns to gaining promotion to the Championship.
"Portsmouth is a great club, whatever division it is in, it is one of major clubs in the country," boss Kenny Jackett told BBC Sport.
"We are close to the promotion places and it is a big two months coming up.
"We are proud of what we have done in the FA Cup. We were the last League One side in it and it has taken a genuinely big club to knock us out."
Reuters contributed to this report.