Goals from Giuseppe Rossi and Nolberto Solano eased Newcastle into the Carling Cup fourth round.
Rossi scored the opener just after half-time
Just over two minutes into the second half Pompey failed to clear Solano's free-kick and Rossi turned well before scoring with a low, left-foot strike.
Substitute Damien Duff then crossed for Solano to head past David James for a second goal five minutes later.
Pompey had a goal disallowed before Solano got on the end of a James Milner cross to add a third from close range.
The win will relieve some of the pressure on Newcastle manager Glenn Roeder, whose side are showing some form as a cup team this season.
Whatever he said at half-time seemed to do the trick after a first half in which neither side were able to come to terms with the driving rain.
The wet conditions almost embarrassed Steve Harper inside three minutes but the keeper recovered well to keep out Matthew Taylor's long-range effort.
Titus Bramble did well to deny former Newcastle striker Andy Cole a clean sight on goal while at the other end Obafemi Martins took advantage of a slip by Linvoy Primus but his chip landed on the roof of the net.
Lomana LuaLua blew a glorious opportunity after beating the offside trap when his poor touch denied him a chance on goal.
Milner and Martins both went close again just before half-time. But shortly after the interval Rossi showed why he is rated so highly at Manchester United when the on-loan striker made room for himself to fire past James.
Duff, who had come on for Martins at half-time, made an almost immediate impact when he swung in a cross from the left for Solano to power home.
Pompey were a beaten side, while the home fans were treated to the first sight of Kieron Dyer since April.
He could have marked his return with a goal within three minutes of entering the fray but drilled his shot across the face of the goal after a fine run.
Pompey had a goal disallowed that could have made for an interesting final five minutes but LuaLua was judged to be offside.
Newcastle manager Glenn Roeder on Giuseppe Rossi:
"He has been very patient waiting for an opportunity. He will certainly get plenty of opportunities between now and the end of December.
"It was a fantastic finish. I would expect him to finish there because I have seen it so often.
"I have seen it in games when he was at Manchester United, whether it was his opportunities in the first team or in reserve-team football.
"He is, in my opinion, a natural goalscorer, and he worked so hard for the team as well. He was a real pain for their defence."
Portsmouth boss Harry Redknapp:
"At half-time I didn't think there was any way we weren't going to go ahead and win.
"I told the lads the game was there to be won.
"I can't say anything about the conditions because that would sound like I'm making excuses. Saturday is a big game now and we have to get a few players fit for that."
Newcastle: Harper, Taylor (Ramage 90), Moore, Bramble, Babayaro, Solano, Butt (Dyer 60), N'Zogbia, Milner, Rossi, Martins (Duff 46).
Subs Not Used: Srnicek, Luque.
Goals: Rossi 48, Solano 53, 90.
Portsmouth: James, Pamarot, O'Brien, Primus, Taylor, Thompson (Koroman 46), Davis (Hughes 73), Fernandes, Kranjcar (Douala 63), Cole, LuaLua.
Subs Not Used: Kiely, Kanu.
Booked: Thompson, Davis.
Ref: A Marriner (W Midlands).