They appeared to be cruising to three points at Glanford Park, with goals from Tom Naylor and Gareth Evans giving them a comfortable interval lead.
But Evans missed a great chance to extend the advantage further after the break and Lee Novak immediately reduced The Iron’s deficit.
The hosts applied some under intense pressure in the closing stages, but the Blues held on to secure more away-day joy for the travelling support.
Kenny Jackett stuck with the same side that comfortably progressed in the FA Cup at Maidenhead a fortnight ago.
It mean that the in-form Oli Hawkins continued to lead the line, having netted five goals in his previous six appearances.
Brett Pitman recovered from a slight knee problem to take his place on the bench, but there was no room for the fit-again Andre Green.
Pompey looked in control for much of the first half and dominated possession, with plenty of the action taking place in and around the opposition area.
There were not too many clear-cut chances at either end of the pitch, although some dangerous deliveries from Jamal Lowe were just out of reach for his team-mates.
Nathan Thompson made a timely block to deny Andy Dales at the other end, while Funso Ojo injured himself as he blazed wildly over and had to be replaced.
A corner from Evans was glanced agonisingly past the post by Matt Clarke and Hawkins then had appeals for a penalty turned down following an apparent push by Cameron Burgess.
Scunthorpe’s best opening came when George Thomas’ corner was nodded narrowly over the bar by Matthew Lund.
Evans almost caught out Jak Alnwick with a set-piece of his own that came close to dipping under the bar before the keeper turned it over.
But the next corner did lead to a goal on 34 minutes, as Jack Whatmough turned Ronan Curtis’ cross back into the centre, where NAYLOR was left in space to hook home.
Pompey were in control by this point and it came as no surprise when they doubled their lead soon after.
Nathan Thompson fed EVANS and the skipper showed neat footwork in the box before lofting a fine shot past Alnwick.
The only sour note for the visitors before the break came when Hawkins was booked following an aerial challenge.
Scunthorpe United 0
The Blues picked up where they left off following the interval and Lee Brown’s free-kick was not too far over the bar after Hawkins had been fouled.
Scunthorpe started to enjoy more of the ball as the second half progressed, although it was still their opponents looking more dangerous.
And Evans should really have wrapped things up on 58 minutes, somehow firing wide from just a few yards out after being picked out by Naylor.
The Iron made Pompey pay for that miss just moments later, with Novak arrowing the ball into the net after Craig MacGillivray had pushed clear Thomas’ cross.
More goals were looking possible at both ends by this point and it was the visitors’ time to go close on 66 minutes.
Alnwick failed to hold a low cross from Lowe under pressure from Evans, but dived on the loose ball before Curtis could capitalise.
There were hearts in mouths at the opposite side of the pitch, with a mad scramble in the Blues box before Whatmough eventually hacked clear.
And another spell of sustained Iron pressure finished with Thomas curling a shot past MacGillivray’s grasp, but also the post.
Jackett was forced to make a change on 79 minutes, with Evans limping off to be replaced by Christian Burgess and a switch to three at the back.
It was proving to be a nervy finale and a free-kick from Thomas somehow evaded everyone on its way out of play, although referee Martin Coy spotted a slight Pompey touch.
But the Blues managed to see out five minutes of stoppage-time, much to the delight of the 913 fans who had travelled up from the south coast,
Scunthorpe (4-1-4-1): Alnwick; McArdle (c), Goode, Burgess, Borthwick-Jackson (Butroid 46); Horsfield (Humphrys 75); Lund, Ojo (Ugbo 13), Thomas, Dales; Novak
Goals: Novak 60
Booked: Goode, Lund, Novak, McArdle
Subs not used: Flatt, Ben El-Mhanni, Morris, Wootton
Pompey (4-2-3-1): MacGillivray; N.Thompson, Whatmough, Clarke, Brown; B.Thompson, Naylor; Lowe (Wheeler 84), Evans (c) (Burgess 79), Curtis; Hawkins
Goals: Naylor 34, Evans 40
Booked: Hawkins, Curtis
Subs not used: McGee, Walkes, Haunstrup, Close, Pitman
Referee: Martin Coy
Attendance: 4,365 (913 Pompey fans)