When the in-form Ronan Curtis headed them in front towards the end of the first half it seemed as though the Blues would continue their climb up the League One standings.
But Ellis Harrison nodded into his own net just before the break, with a finish that would have been lauded at the other end of the pitch.
And Stanley ran away with it after the break, with Dion Charles giving them the lead – albeit in controversial circumstances – before Colby Bishop added a brace.
Kenny Jackett made five changes from the side that drew with Peterborough on home soil the previous week.
The entire defence had to change, with Brandon Haunstrup (knee) and Lee Brown (Achilles) both injured, Christian Burgess suspended and Oli Hawkins recently becoming father to a baby boy.
That meant there were recalls for James Bolton and Anton Walkes in the full-back slots and Sean Raggett in the middle, while Tom Naylor also dropped into the back-line.
Ross McCrorie took the skipper’s midfield slot and Ryan Williams dropped to the bench to make way for Marcus Harness on the right.
Pompey started brightly and were camped out in their opponents’ half in the opening stages, but created only one decent opening.
Harrison’s cross from the left was just behind a stretching John Marquis, who could only send the ball over the bar and out of the ground.
Stanley then started to apply more pressure as the first half progressed and Jordan Clark was inches away from making a connection when he slid in at the far post.
Bishop was next to go close flashing a shot narrowly wide after Ben Close had initially made a fine challenge on Sam Finley.
It took a decent tackle from Ross Sykes to deny Marquis at the other end, with the striker almost being sent through by Harrison.
The hosts were still looking more dangerous, though, and when Clark met Seamus Conneely’s cross from deep on the left, Craig MacGillivray was forced to make a fine save to tip the ball over.
Pompey then started to pick up again, although Harrison and Marquis collided with Mark Hughes when all three players tried to get to Harness’ centre first.
Bolton was then unable to get enough on Curtis’ free-kick from the left and Josef Bursik made a simple stop.
But the Blues did go ahead on 35 minutes, as Harness whipped in a dangerous cross from the right and CURTIS stooped to meet it, sending the ball into the net off the inside of the post.
Jerome Opoku came close to hitting an immediate leveller, courtesy of an audacious long-range piledriver that cannoned back off the post.
And Accrington did equalise just before the break – although they received a big helping hand from the visitors.
Conneely sent a corner into the box and Harrison rose to meet it with a firm header that inadvertently sent the ball past MacGillivray and into his own net.
Accrington Stanley 1
The hosts had unsuccessfully appealed for two penalties before the break and were at it again when the action restarted.
This time it was Clark who felt he was unfairly upended by Walkes, but referee Martin Coy remained unimpressed.
Pompey then came close to retaking the lead when Harrison turned quickly outside the box and hit a fine strike that a diving Bursik did well to push clear.
Raggett soon did well at the other end to hold off Charles and stop the striker going one-on-one with MacGillivray.
But Charles did give Accrington the lead just past the hour mark, although the hosts were unhappy that the goal was allowed to stand.
Opoku held off Harness with a hand to the face, but it was not spotted by Coy and the left-back was able to square for his team-mate to slot home.
Jackett responded with a double change, as Harness and Marquis made way for Williams and Brett Pitman.
But Stanley almost extended their advantage just seconds later, as Bishop glanced a header against the post, with the loose ball hacked clear.
And Bishop did give them a cushion on 69 minutes, angling the ball into the net after MacGillivray had parried clear Finley’s initial effort.
Things soon got even worse for the visitors, as Bishop raced clear to slot home his second goal of the afternoon.
That came after Coy had played advantage following McCrorie’s challenge on Charles, but the referee went back to book the midfielder.
Accrington continued to look threatening as the minutes ticked down, while a neat Pitman flick was blocked before it could trouble Bursik.
That was as close as Pompey came to reducing their deficit, although the 733 travelling fans continued to cheer right up until the final whistle.
Accrington (4-4-2): Bursik; Johnson, Sykes, Hughes, Opoku; Clark, Finley (Diallo 90), Conneely (c), Pritchard; Bishop (Zanzala 90), Charles
Goals: Harrison 44 (og), Charles 62, Bishop 69, 77
Subs not used: Evtimov, Alese, Rodgers, Sherif, Carvalho
Pompey (4-2-3-1): MacGillivray; Bolton, Naylor (c), Raggett, Walkes; McCrorie, Close; Harness (Pitman 65), Marquis (Williams 65), Curtis; Harrison
Goals: Curtis 35
Subs not used: Bass, Downing, Casey, Cannon, Evans
Referee: Martin Coy
Attendance: 2,429 (733 Pompey fans)