The home side appeared to have got the job done with a brace from Harvey Knibbs early in the second half.
A Michael Jacobs header gave the Blues hope of a comeback, but there was to be no late drama at Abbey Stadium.
Danny Cowley made five changes from the side that dramatically beat Exeter on Friday night to reach the last 16.
There was a welcome return for skipper Clark Robertson, who made his first appearance in exactly four months after recovering from a hip injury.
Ronan Curtis started following his heroics from the bench in Devon, while there were also places for Louis Thompson, Reeco Hackett and Jacobs.
Sean Raggett, Lee Brown, Miguel Azeez, Marcus Harness and John Marquis all dropped to the bench, where they were joined by a fit-again Ryan Tunnicliffe.
Both teams showed an intent to get forward in the opening stages, with chances arriving at either end of the pitch.
Sam Smith raced in behind the defence to meet a deep Wes Hoolahan cross, but Alex Bass made a fine save to tip the ball over.
The keeper had an easier stop to make a few moments later, with Knibbs firing straight at him.
It was Pompey’s turn to attack soon after and Curtis scuffed a shot past the post after his initial attempt had been blocked.
George Hirst’s touch from a Hackett free-kick was then just too heavy, allowing Dimitar Mitov to gather.
But the quality started to wane as the action progressed, with each side cancelling the other one out.
Kieron Freeman did well to deal with the danger after Hoolahan skipped past a couple of half-hearted challenges.
Meanwhile, a spell of promising Blues pressure eventually broke down when Curtis nodded a cross wide.
And a low long-range effort from Jacobs was struck cleanly enough, only to fly straight into Mitov’s midriff.
Cambridge United 0
Robertson’s work was done for the night, with the captain replaced in the centre of defence by Raggett.
It was Cambridge who made the brighter start to the second half, however, and enjoyed a period of pressure that led to their breakthrough.
The ball ricocheted kindly for Knibbs on the edge of the box and he hit a precise shot that flew past Bass and nestled in the bottom corner.
And the home side continued to dominate, with Knibbs nodding them further into the lead after Hoolahan had lifted a pass into the mixer.
Cowley’s response was to make another quartet of substitutions, as Tunnicliffe, Brown, Marquis and Harness replaced Thompson, Hackett, Hirst and Curtis.
But it was still United looking more likely to add to the scoring and Jack Lankester curled a free-kick narrowly over the bar.
Bass then made three saves in quick succession to deny Harrison Dunk and James Brophy from tight angles, and then a more central effort from Lankester.
The ball was finally put in the back of the net by Knibbs, but referee Darren Drysdale had spotted an infringement.
And the Blues suddenly found themselves back in the contest, as JACOBS rose to nod home a Brown corner, despite the best efforts of Liam Bennett to clear from the line.
That perked the visitors up and they set about trying to find another late goal in the Papa John’s Trophy.
They were not too far away when a cross from Jacobs was deflected onto the head of Marquis and the ball fizzed past the post.
Brown then saw a shot blocked after being teed-up by Jacobs, as the Blues tried to force a penalty shoot-out.
They came even closer when Harness swung the ball into the box from the left and Marquis prodded it straight into the arms of Mitov.
And Cambridge were able to see out six minutes of stoppage-time to seal a quarter-final trip to Rotherham.
Cambridge (4-2-3-1): Mitov; Bennett, Okedina, Iredale, Dunk (c); O’Neil (Worman 46), May (Digby 71); Lankester (Dickens 90+1), Hoolahan (Brophy 71), Knibbs (Ironside 83); Smith
Goals: Knibbs 50, 59
Booked: Lankester, Iredale
Sub not used: Mannion
Pompey (3-4-1-2): Bass; Freeman, Robertson (c) (Raggett 46), Ogilvie; Romeo, Thompson (Tunnicliffe 60), Morrell, Hackett (Brown 60); Jacobs; Hirst (Marquis 60), Curtis (Harness 60)
Goals: Jacobs 76
Subs not used: Steward, Azeez
Referee: Darren Drysdale
Attendance: 1,308 (283 Pompey fans)