The visitors had several chances to score before the break, but would have been happy to go in level after Craig MacGillivray conceded and saved a Billy Kee penalty.
Oli Hawkins finally broke the deadlock in the second half, only for Michael Ihiekwe to level seconds later.
Kenny Jackett made four changes from the side that drew with Burton earlier in the week.
Gareth Evans returned to skipper the team in place of the injured Dion Donohue, with Ben Close replacing the suspended Tom Naylor.
There were also a couple of alterations at the back, with Anton Walkes and Jack Whatmough dropping to the bench to make way for Nathan Thompson and Christian Burgess.
Pompey dominated the opening stages and created several decent opportunities as they tried to break the deadlock.
Jamal Lowe was a particular thorn in Stanley’s side, but could not beat keeper Connor Ripley after showcasing some tricky footwork in the box.
The resulting corner from Evans found its way to Ben Thompson and his acrobatic effort flew narrowly wide.
It was Evans who was next to try his luck and a fierce effort on the volley from outside the box was palmed wide by the busy Ripley.
There was not much happening at the other end, although a weak effort from Kee was comfortably held by MacGillivray.
But it was soon the Blues back on the attack and Ronan Curtis’ long-range strike flashed past the post.
It was pretty much one-way traffic and Lowe’s first-time shot from the edge of the box was again kept out by Ripley.
The keeper was certainly earning his wage and saved an angled drive from Curtis as the visitors continued to apply pressure.
And the Irish forward went even closer when he rose at the far post to meet Lowe’s cross, only to see his header cannon back off the post.
But Accrington came into the game more as the half progressed and should have broken the deadlock on 33 minutes.
MacGillivray failed to hold on to a corner and in his eagerness to recover the ball, brought down Kee inside the box.
Referee Stephen Martin did not need much convincing that a foul had been committed, immediately pointing to the spot.
But MacGillivray quickly redeemed himself, flinging himself to the right to palm Kee’s penalty to safety.
And the keeper came to the rescue again before the break, denying the same player from converting a corner at the far post.
Accrington Stanley 0
The second half started with Nathan Thompson earning a yellow card from Martin for a foul on Offrande Zanzala.
It was the right-back’s fifth League One booking of the season, meaning he will miss next Saturday’s trip to Bradford.
Pompey needed some time to find their feet following the restart, but almost took the lead just before the hour mark.
Lowe won a corner and when it was only partially cleared, a volleyed attempt from Curtis cannoned off the crossbar.
Pompey did forge ahead moments later, however, when Evans whipped a free-kick into the box and HAWKINS stuck out a boot to force the ball home.
But the lead was short-lived and Stanley levelled from a set-piece of their own, as Ihiekwe rose to convert Sean McConville’s delivery.
Those goals aside, however, the second half had not been as incident-packed as the first, with both sides lacking a quality final ball.
Brett Pitman replaced Hawkins for the final 10 minutes in an attempt to inject some fresh attacking impetus.
But neither side particularly looked like scoring in a drab conclusion to a contest that had promised so much more.
Stanley substitute Connor Hall did draw a save from MacGillivray in stoppage-time, but the hosts could not capitalise on the loose ball and the game finished all square.
Accrington (4-4-2): Ripley; Johnson, Ihiekwe, Hughes, Anderton; Mingoia, Barlaser, Finley, McConville (c); Zanzala (Hall 88), Kee
Goals: Ihiekwe 64
Subs not used: Maxted, Richards-Everton, Sykes, Conneely, Brown, Mangan
Pompey (4-2-3-1): MacGillivray; N.Thompson, Burgess, Clarke, Brown; Close, B.Thompson; Lowe, Evans (c), Curtis; Hawkins (Pitman 81)
Goals: Hawkins 62
Subs not used: McGee, Walkes, Whatmough, Haunstrup, Wheeler, Mason
Referee: Stephen Martin
Attendance: 3,558 (1,163 Pompey fans)