It was a scintillating first half performance – and one particular moment of brilliance – that did the damage.
Kyle Bennett ensured that the Blues made the most of their early dominance by firing them ahead and Matty Pearson’s unfortunate own-goal added to the travelling supporters’ glee.
But they were even happier when a stunning strike from Michael Doyle secured the three points before the interval.
Shay McCartan did grab a late consolation for the hosts, but that failed to dampen the mood of those making the long trip home to the south coast.
Paul Cook made one change from the side that won at Stevenage at the weekend.
It was a straight swap up front, with Michael Smith coming in to lead the line and Marc McNulty dropping to the bench.
Pompey totally dominated the first half, with Gary Roberts pulling the strings for the visitors in midfield.
He even tried a cheeky attempt from just inside the opposition half after just four minutes, although the shot did not overly trouble Jason Mooney in the Stanley goal.
Roberts went closer moments later, though, meeting Ben Davies’ cross with a near-post header that flew into the keeper’s arms.
And he was involved when the Blues did deservedly break the deadlock midway through the first half.
Roberts linked up well down the left with Gareth Evans and when the latter’s low cross was only partially cleared, BENNETT drilled home a low shot off the inside of the post.
Accrington were not causing too many problems at the other end, although Ryan Fulton did make a regulation save to deny Billy Kee.
The visitors were soon back on the attack, however, and Doyle rattled the crossbar with a fierce shot after shaking off a clumsy challenge from Matt Crooks.
Pompey deserved to forge further ahead, but the second goal on 36 minutes did arrive in fortunate fashion.
Danny Hollands picked out Davies with a fine cross-field pass and the right-back’s low delivery was inadvertently turned into his own net by PEARSON.
Piero Mingoia prevented things from getting even worse for the hosts when he just about got to Smith’s cross before Bennett could reach it.
But there was nothing that anybody could do to keep out Pompey’s third goal just before the break.
It was a goal of the season contender from DOYLE, who lashed in an unstoppable 25-yard volley after a free-kick was not properly dealt with.
The Blues skipper was mobbed by his team-mates, while even the beleaguered home support applauded a moment of magic.
Accrington Stanley 0
Accrington replaced skipper Seamus Conneely with Scott Brown in an attempt to get back into the game.
It was still the visitors causing more problems, though, and Pearson had to turn a dangerous Bennett cross behind before it could reach the lurking Smith.
But the Stanley centre-back then almost grabbed his second own-goal of the evening while trying to deal with Davies’ cross, with Mooney just about managing to divert the ball over.
The hosts were looking more of a threat since the restart and there were half-chances for both McCartan and Kee.
Pompey were also proving dangerous going forward, however, and Smith turned Enda Stevens’ low cross narrowly wide on the hour mark.
Cook made his first switch on 73 minutes, with the hard-working Smith making way for McNulty up front.
He then replaced one former Accrington player with another, as Kal Naismith came on for the impressive Roberts.
And Naismith immediately looked to add to the Blues’ lead when he burst forward down the right, but was unable to bend his shot past Mooney.
Pompey looked to be coasting to the final whistle, but Stanley did reduce the deficit when McCartan spun inside the area and slammed the ball home.
That raised a few nerves, but Doyle almost calmed them when Mooney’s clearance landed at his feet and the midfielder’s effort from the halfway line was only just scrambled away by the keeper.
But the Blues had already done enough to secure all three points and leapfrog their opponents into fourth spot.
Accrington (4-2-3-1): Mooney; Wakefield, Davies, Pearson, Halliday; Crooks, Conneely (c) (Brown 46); Mingoia (Boco 67), McCartan, McConville (Shaw 67); Kee
Goals: McCartan 83
Subs not used: Hughes, Procter, Carver, Steenson
Pompey (4-2-3-1): Fulton; Davies, Burgess, Webster, Stevens; Hollands, Doyle (c); Evans, Roberts (Naismith 78), Bennett (Freeman 83); Smith (McNulty 73)
Goals: Bennett 22, Pearson 36 (og), Doyle 43
Subs not used: Bass, Clarke, Barton, Chaplin
Referee: Stephen Martin
Attendance: 1,841 (584 Pompey fans)