It was a deserved outcome, although the hosts probably should have made life easier for themselves following a dominant first half display.
Sean Raggett headed them in front and Michael Jacobs continued his fine individual form by doubling the leas before the break.
But former Fratton loanee Gassan Ahadme reduced Albion’s deficit shortly after the restart, meaning the rest of the contest was nervier than it might have been.
Danny Cowley made two enforced changes from the side that were cruelly beaten at Oxford at the weekend.
Joe Morrell saw his appeal for a harsh sending off dismissed, so began a three-match ban and made way for Tyler Walker.
The other switch was like-for-like, as Mahlon Romeo recovered from an ankle injury to replace Kieron Freeman, who was suffering from concussion.
Pompey came tearing out of the blocks and there were just 35 seconds on the clock when they had a chance to opening scoring.
Hayden Carter got free and found Ronan Curtis, who escaped one challenge before seeing his effort deflected wide.
Jacobs then found space to get forward and hit a low shot that was parried clear by Ben Garratt, with William Kokolo mopping up the loose ball.
The resulting corner was sent into the mixer by Jacobs, but Connor Ogilvie could only get a glancing touch.
There was a drop in pace after that flurry of activity, with the match turning into a slightly cagey affair.
But the Blues started to get back on top and a lovely ball from George Hirst started an attack, but he could only head over when the cross came in from Jacobs.
The pair combined again moments later, swapping passes in the area before the Leicester loanee’s shot was deflected behind.
And it was from the resulting corner that the deadlock was broken, as RAGGETT rose highest to head home Jacobs’ delivery.
It came as no surprise to see that man JACOBS double the lead before the break, catching Joe Powell dithering and nipping in to slot the ball past Garratt.
Burton did have an opportunity to reduce their deficit before the whistle blew, with Gavin Bazunu having to get down to deal with Ciaran Gilligan’s strike.
Burton Albion 0
The hosts looked to keep attacking once the action restarted, only for their opponents to find a lifeline.
Mahlon Romeo and Carter got in each other’s way as the ball ran across the box and Terry Taylor’s angled effort was turned home by Gassan.
Powell then tried to sneak a free-kick inside Bazunu’s near post, but was unable to keep his effort down.
Pompey were struggling to replicate the attacking fluency on display at times before the break, although a Jacobs corner caused problems in Brewers box before eventually being hacked clear.
And they came close to restoring their two-goal lead on 67 minutes after Louis Thompson’s persistence had found Jacobs in space.
His low centre was only cleared as far as Curtis, whose shot was turned over the bar by the leg of Garratt.
The keeper then came off his line to deny Walker a first Blues goal after the ball had been flicked on by Hirst.
But Burton had a chance of their own moments later, with Ogilvie having to time his tackle to perfection to dispossess Harry Chapman inside the box.
Cowley then decided to add some fresh legs in the midfield engine room, as Thompson made way for Ryan Tunnicliffe.
And a second substitution followed soon after, with Denver Hume replaced on the left by Reeco Hackett.
There were comical scenes when a decision went against the visitors, leading to their manager Jimmy Floyd Hasselbaink throwing his papers in the air and jumping up in frustration.
He was shown a yellow card for his outburst by referee Craig Hicks, while Clark Robertson came on for Jacobs during the pause in play.
And the Blues then saw out the closing stages with relative ease to climb above their opponents in the League One standings.
Pompey (3-4-1-2): Bazunu; Carter, Raggett (c), Ogilvie; Romeo, Thompson (Tunnicliffe 73), Jacobs (Robertson 85), Hume (Hackett 80); Curtis; Hirst, Walker
Goals: Raggett 33, Jacobs 41
Booked: Raggett, Curtis
Subs not used: Webber, Jewitt-White, Harness, O’Brien
Burton (3-4-3): Garratt; Shaughnessy, Leak, Borthwick-Jackson; Hamer, Mancienne (c) (Saydee 82), Taylor (Chapman 63), Kokolo; Gilligan, Gassan (Moult 86), Powell
Goals: Gassan 50
Booked: Mancienne, Powell, Taylor, Chapman
Subs not used: Kovář, Blake-Tracy, Maddox, Lakin
Referee: Craig Hicks
Attendance: 13,407 (96 away fans)