The visitors were outplayed in the first half when Matt Clarke and Marc McNulty scored to put the promotion chasers in control and Portsmouth threatened with just about every attack.
Reds made more of a game of it in the second half and Gwion Edwards was inches away from reducing the deficit with a free kick which hit the bar.
Instead, Gary Roberts made it 3-0 with ten minutes to go while Reds lost both Josh Yorwerth and Jimmy Smith to first-half injuries.
Manager Mark Yates made three changes with Matt Harrold, Luke Rooney and goalkeeper Darryl Flahavan returning to the side. Lee Barnard (ribs) was sidelined through injury and Jon Ashton and Callum Preston dropped to the bench.
And the visitors, backed by a noisy contingent of fans in the Milton End, began the game promisingly with the first ten minutes played predominantly in the Portsmouth half.
But slowly the tide began to turn. Pompey’s full backs Ben Davies and Edna Stevens took every opportunity to get forward in support of their wide attacking players and Reds found themselves behind in the 13th minute. Once again they were undone by a set piece as defender Clarke got in front of Josh Yorwerth to meet Davies’ inswinging flag kick and guide an unstoppable header past Flahavan.
For the next 30 minutes or so Reds found themselves under the cosh as Pompey created chance after chance. McNulty fired wide on 14 minutes, Clarke headed another Davies corner just wide, Stevens flashed the ball across the face of goal which only needed the slightest touch to go in, Lewis Young made a crucial block to deny ex-Reds’ loanee Kyle Bennett, who then saw a shot deflect off Jon Ashton and force Flahavan to make a scrambling save.
Ashton had come on midway through the half for Yorwerth, who limped off injured, but it was no surprise when Pompey doubled their lead in the 27th minute. Stevens’ cross took a deflection and landed conveniently at the feet of McNulty six yards out and he had time to switch it onto his right peg before firing past Flahavan.
At that stage Pompey looked like scoring every time they attacked. Mark Yates responded to the onslaught by switching to 4-4-2 with Smith moved to the right of midfield to give Lewis Young more protection and Roarie Deacon pushed up alongside Harrold.
The change did allow Reds to finally get a foot hold in the game and just before the break Deacon and then Simon Walton, with a 30-yard free kick, finally forced Brian Murphy to get his hands dirty.
But Pompey ended the half firmly in control and Clarke should have scored their third, but headed wide unmarked from a corner after getting between Walton and skipper Sonny Bradley.
Reds made their second change at the break when Josh Emmanuel replaced Smith, who had taken a knock before the break, with Young moving into right midfield.
Bennett cut inside to fire just over Flahavan’s bar in the 50th minute but Reds went close to pulling one back in the 63rd minute. Davies was penalised for a foul on Edwards 25 yards out and the Welshman curled the free kick over the wall and against the bar with Murphy beaten.
The home side did not start the second half with the forward momentum they had shown for much of the first and Reds were able to enjoy some decent spells of possession either side of that near miss.
Harrold would have buried Hancox’s cross had Michael Doyle not taken the ball off the striker’s head but Pompey were still a threat. Midway through the half Young cleared a thumping header from Caolan Lavery off the line.
Lavery glanced his header from Bennett’s cross wide but Reds had given a much better account of themselves in the second half with Clarke needing to clear his lines hurriedly to stop Harrold from getting on the end of Edwards’ cross.
Gavin Tomlin replaced Rooney with 15 minutes to go and with his first touch guided a stooping header from Emmanuel’s cross into the hands of Murphy then Young broke into the box and found Harrold but, on the stretch, the striker’s shot went wide of the left-hand post.
But with ten minutes to go Pompey sealed their win. Edwards’ corner was headed clear and substitute Ben Tollitt picked up possession and ran 70 yards into the Reds’ half before unselfishly setting up fellow sub Gary Roberts who slid the ball past a helpless Flahavan.
Reds now have back-to-back home games to kick-start their year with Cambridge United at the Checkatrade.com Stadium next Saturday.