He struck in the second minute of each half, then wrapped up the three points with a fine turn and finish.
The first of his goals had been cancelled out by Lucas Akins, while Tom Naylor soon found his own net to ensure the Brewers led at the break.
But Harness – facing his former club – quickly levelled and, after Jack Whatmough had given the Blues the lead, finished things off to claim the matchball.
Kenny Jackett made two changes from the side that were beaten on home soil by Wigan the previous weekend.
Ellis Harrison returned to lead the line, while there were also starts for Lee Brown and Ryan Williams.
John Marquis, Cam Pring and Ronan Curtis all dropped to the bench, with the latter looking to make his 100th appearance for the club.
The visitors got off to a blistering start in the wet and windy conditions, taking the lead with just 79 seconds on the clock.
Michael Jacobs showed neat footwork in the box, but was tackled as he shaped to shoot and the ball fell for HARNESS to drill home.
The advantage should probably have been doubled moments later, with Williams racing through on goal and bending his shot the wrong side of the post.
Instead it was the Brewers who got the next goal of the game when Ryan Edwards cut the ball back for Kane Hemmings.
His effort was blocked by Tom Naylor, but the follow-up from Akins was deflected in off the Pompey skipper.
And there was more misfortune for the midfielder when he tried to clear Joe Powell’s cross and inadvertently sliced the ball into his own net to give Burton the lead.
The Blues tried to hit back and Harrison was perhaps a bit too eager, earning a booking for a crunching challenge on Ben Fox.
Jacobs was looking the most dangerous outlet down the left, but the visitors were just missing that final ball.
Williams did combine well with Harness on 35 minutes and the latter’s drive flew narrowly past the post.
Harness then had a great chance to level deep into stoppage-time, when Williams’ cross was parried into his path by Ben Garratt, but he was unable to convert from close range.
Burton Albion 2
The visitors came charging out of the blocks following the restart and Harrison’s header was just about diverted wide by Garratt.
But an equaliser did arrive from the resulting corner, with HARNESS neatly back-heeling the ball home after Harrison had initially got his head to Brown’s delivery.
Harrison tried to restore the lead after receiving a lovely lifted pass from Naylor, but – under pressure from two defenders – could only hook over the bar.
Then, when the striker was brought down 20 yards out, Jacobs curled the free-kick onto the roof of the net.
It seemed only a matter of time before Pompey would score again and when two defenders collided, Harrison drew a smart save from Garratt.
The resulting corner did lead to a goal on the hour mark, though, as Brown’s cross was nodded back into the mixer by Harrison for WHATMOUGH to slot home.
Jackett soon made his first change of the afternoon, with Curtis bringing up his Blues century by replacing Williams.
Pompey were winning plenty of corners and another one ended with Harrison drawing a save from Garratt.
They were looking completely dominant and so it came as no surprise when the fourth arrived on 74 minutes.
Curtis played the ball across to HARNESS, who beat his man with a delightful flick before lifting the ball over Garratt.
He then turned provider to create an opportunity for Curtis, but the Republic of Ireland international saw his effort blocked.
Harrison was given warm applause by the Blues bench as he made his way off and Marquis came on for the final few minutes.
And it was a similar story when Harness made way for Andy Cannon, as the closing stages were negotiated with ease to ensure Pompey broke their duck and leapt up the table.
Burton (4-1-4-1): Garratt; Fox, Brayford (c), O’Toole, Daniel; Quinn (Roles 66); Akins, Edwards, Powell (Lawless 80), Vernam (Vassilev 66); Hemmings
Goals: Akins 14, Naylor 20 (og)
Subs not used: O’Hara, Wallace, Gallacher, Gilligan
Pompey (4-2-3-1): MacGillivray; Johnson, Whatmough, Raggett, Brown; Naylor (c), Morris; Williams (Curtis 62), Harness (Cannon 90), Jacobs; Harrison (Marquis 86)
Goals: Harness 2, 47, 74, Whatmough 60
Subs not used: Bass, Nicolaisen, Pring, Close
Referee: Tom Nield