Kevin van Veen had given the away side the lead in the first half after he headed home a Stephen Dawson cross, before Neal Bishop bundled home a second late on to seal the points and prevent a nervy ending.
The side was unchanged from the one that had defeated Oldham Athletic 1-0 at Glanford Park on Saturday, but Paddy Madden did return to the bench after sitting out the Latics game with a minor injury.
The Iron went into their League One encounter at the in-form Posh looking to keep their six-point gap between themselves and the chasing cap.
United started the game brightly, and forged a great opening after only two minutes through Kevin van Veen. But, as he cut in and curled his shot, it was a comfortable height for Luke McGee to parry away to safety.
A thoroughly confident start to the game was capitalised on by van Veen in the 20th minute, as he headed home from Stephen Dawson’s pin-point cross to give the away side a deserved lead.
The opening goal didn’t mean the Iron would stop the intensity of their play, with a Conor Townsend effort from 30-yards out deflected wide after 30 minutes. The resulting corner came to nothing, though.
Three minutes before the break, the Iron carved out another half chance when Townsend laid the ball into the path of Duane Holmes – but his low effort from the edge of the box was well held onto by McGee.
Two additional minutes were added on at the end of a great half for United and, just a few seconds into that added time, they were given the chance to whip a ball in from a free kick on the touchline. The kick was taken and Tom Hopper looked to have been pushed over outside the box, but the referee said no and the ball rolled out harmlessly. That would be the last action of the half, with the scoreline at 1-0 to the Iron.
The first opportunity of the second half went the hosts’ way as Chris Forrester found the space to let rip, but Luke Daniels had the composure to let it fly over.
It only took the Posh another minute to carve open a wonderful opportunity, but Michael Smith scuffed his shot in the penalty area when really he should have been at least making Daniels work.
From that Posh attack Dawson picked up an injury, and unfortunately had to make way for Richie Smallwood.
Morris’ shot on 54 minutes was deflected out for a corner, which Holmes delivered onto the head of Murray Wallace, but the Scotsman couldn’t keep his effort down.
Posh came agonisingly close to an equaliser on the 59th minute. Nicholls’ ball across the face of the Iron goal was perfect, but there was thankfully no one in blue to tap home.
Almost immediately up the other end it was the Iron’s turn to come close as Morris’ corner was headed over the bar by Neal Bishop.
The next opportunity after 66 minutes would be a Scunthorpe one, but substitute Richie Smallwood’s sweet strike rose too much, though it had McGee scrambling.
Nicholls then missed a glorious opportunity for the hosts but, after Marcus Maddison’s shot was parried into his path, he failed to control his diving header.
Substitute Sam Mantom could have doubled the Iron’s lead on 78 minutes after he had the time to get an effort off in the box, but that chance went wide.
United did double their lead in the 82nd minute however, and it was Bishop who got it. Morris’ corner was headed by Bishop, but saved – then Charlie Goode had an effort saved, but it fell kindly for Bishop who bundled home to give the visitors a much more comfortable scoreline of 2-0.
That Bishop goal would be the last notable effort of the game as the Iron superbly saw the game out to confirm a fifth successive league win.
Peterborough United: McGee, Smith, Hughes, Bostwick (Moncur, 66), Tafazolli, Baldwin, Forrester, Maddison, Coulthirst (Edwards, 46), Da Silva Lopes (Angol, 46), Nichols.
Substitutes not used: Tyler, White, Binnom-Williams, Taylor.
Scunthorpe United: Daniels, Wiseman, Wallace, Dawson (Smallwood, 51), van Veen (Mantom, 74), Morris, Bishop, Hopper (Williams, 87), Holmes, Goode, Townsend.
Substitutes not used: Anyon, Madden, Adelakun, Clarke.
Attendance: 5,222 (395 away).