The damage was done in the first half, with goals from Lee Novak and Duane Holmes giving the hosts a commanding lead.
It was a much more assured performance from the Blues after the break, but they did not really do enough to warrant any return for their efforts.
Kenny Jackett made two changes from the side that beat Fleetwood so convincingly at Fratton Park the previous week.
One was enforced, with Damien McCrory’s knee injury affording Dion Donohue a chance at left-back.
The other switch was up front, with Conor Chaplin dropping to the bench to be replaced by Oliver Hawkins.
Just 12 goals had been scored in Scunthorpe’s preceding eight league games and a barren contest looked likely following a cagey opening.
But it was the hosts that were quickest to settle and Paddy Madden flashed an angled drive narrowly past the post.
Pompey then had their first sighter, although Brett Pitman’s cleanly-struck effort flew straight into the arms of Iron keeper Matt Gilks.
Scunthorpe were looking more likely to break the deadlock, however, and Novak chipped a shot against the crossbar after bundling his way into space.
And it was Novak who did give them the lead on 12 minutes, steering home after Jordan Clarke had collected Neal Bishop’s cross-field pass and sent the ball into the box.
The Blues were struggling to find any fluency, although Hawkins had a great opportunity to draw them level.
Jamal Lowe brilliantly beat his man down the right and delivered the ball into the area, only for the striker to head wide from just a few yards out.
And the visitors were made to pay for their profligacy when Scunthorpe doubled their advantage just a few moments later.
Donohue was only able to head Lewis Butroid’s teasing delivery straight to Holmes, who coolly steered the ball past Luke McGee and into the net.
Pompey kept fighting, though, and a couple of Donohue corners caused problems in the Iron defence.
The left-back’s free-kick was then headed into Christian Burgess’ path by Hawkins, but the defender mis-kicked the ball into Gilks’ arms.
However, there was an escape at the other end just before the break when Novak failed to get on the end of another excellent Butroid cross.
Scunthorpe United 2
Pompey, unsurprisingly, came out for the second half with a lot more urgency and Pitman bent a shot narrowly wide following good work from Matty Kennedy down the left.
The hosts then received a blow when Novak when down injured and despite trying to carry on for a few minutes, he was soon replaced by Tom Hopper.
It was the Blues who were dominating possession as the second half progressed, without being able to penetrate the Scunthorpe defence and test Gilks.
A challenge for the ball then saw Matt Clarke become the latest member of the Pompey squad to suffer a cut head and he had to be treated on the pitch by physio Bobby Bacic.
It meant the defender was left with a bandaged head, while Pitman was playing with a broken nose and Hawkins still has a huge scar above his eye.
And it was the latter who made way as Jackett made his first switch on 68 minutes, with Chaplin on to lead the line.
It was Ben Close who was next to try his luck, however, with a volley that was deflected behind after Kennedy’s floated delivery could only be partially cleared.
Jackett made another substitution soon after, as Kennedy was replaced by Kal Naismith wide on the left.
But Scunthorpe threatened to add a third goal on 74 minutes, with a long-range drive from Holmes stinging the palms of McGee.
It was still the Blues playing with more intent, but Gilks was being well protected by an organised Iron back-line.
Burgess was almost the unlikely provider of a goal on 83 minutes, volleying narrowly wide with an acrobatic effort after being picked out in space by Close.
Lowe, unlike last week, was then unable to find the net from a tight angle, as Gilks was finally forced into action.
And Scunthorpe comfortably saw out the closing stages to ensure Pompey made the long journey south without any points.
Scunthorpe (4-4-2): Gilks; Clarke, McArdle (c), Wallace, Butroid; Holmes (Mantom 79), Bishop, Ojo, Morris; Novak (Hopper 54), Madden (Burgess 84)
Goals: Novak 12, Holmes 33
Subs not used: Watson, Sutton, Adelakun, van Veem
Pompey (4-2-3-1): McGee; Thompson, Burgess, Clarke, Donohue; O’Keefe, Close; Lowe, Pitman (c), Kennedy (Naismith 73); Hawkins (Chaplin 68)
Subs not used: Bass, Talbot, Haunstrup, May, Evans
Referee: Anthony Backhouse
Attendance: 4,685 (815 Pompey fans)