There were not abundance of clear-cut chances in a contest that saw both clubs look to continue their late charge for the play-offs.
The Tractor Boys finished stronger, though, and there was relief when a late goal was disallowed for offside.
Danny Cowley made two changes from the side that enjoyed a comfortable win at Crewe earlier in the week.
Aiden O’Brien and Ryan Tunnicliffe both returned to the starting line-up, as Tyler Walker and Joe Morrell dropped to the bench.
There was a familiar face in the opposition ranks, with Pompey academy graduate Conor Chaplin named in the Tractor Boys team.
It was the hosts who saw more of the ball in the opening stages and enjoyed the territorial advantage, without forcing Gavin Bazunu into action.
There was an effort from Chaplin that bobbled past the post, while Cameron Burgess could not quite pick out Kayden Jackson when he met a dangerous Wes Burns delivery.
And the first decent chances fell to the visitors, with a low Ronan Curtis centre taking a deflection and ricocheting off O’Brien before bouncing over.
The Republic of Ireland international then intercepted a poor pass just moments later and drilled a shot narrowly wide.
Louis Thompson was unhappy to be booked for a firm challenge on Burns, when he appeared to win the ball.
And there were a few other free-kick decisions from referee Christopher Sarginson that frustrated the Blues.
Ipswich did threaten to forge ahead with a couple of opportunities just before the break, starting with a 25-yard effort from Chaplin that flew not too far over.
The same player then released Jackson with a superb pass, but Bazunu was quickly off his line to deny the striker.
Ipswich Town 0
There was little to properly excite either set of supporters in an attacking sense immediately after the restart.
A Macauley Bonne header was comfortably claimed by Bazunu, while Burns fired a shot high over the bar.
Pompey were struggling to make any inroads at the other end, although began to get more of a foothold in midfield as the second half progressed.
And two Curtis deliveries in quick succession – one high and the other along the floor – somehow failed to get a touch from anyone as they made their way across the box.
Then a cross from Connor Ogilvie was met by a glancing Sean Raggett header that landed on the roof of the net.
Cowley made a switch on 71 minutes when Thompson went off after receiving some treatment on the pitch and was replaced by Morrell.
There was still not much to test either keeper, although Bazunu got down to his right to make a regulation stop when Theo Bakinson tried his luck from outside the box.
But the Tractor Boys did go close when Bersant Celina took a neat touch to create space and angled in a shot that was well saved by Bazunu.
Burns swung the ball towards the back post just a few moments later and Bakinson’s header flew into the side netting.
Tempers then threatened to boil over on the sidelines and a bout of pushing and shoving had to be calmed down.
It resulted in yellow cards for both Dominic Thompson and Curtis, as well as one for Blues boss Cowley.
Denver Hume replaced O’Brien for the contest’s closing stages, while George Hirst then made way for Walker.
Ipswich thought they had a late winner after Burgess’ header from a Celina free-kick was parried away by Bazunu.
Bonne slammed the loose ball into the net and the ground erupted, only for their celebrations to be cut short by an offside flag.
And Pompey were able to see out four minutes of stoppage-time to collect what could prove to be a valuable point.
Ipswich (3-4-3): Walton; Donacien, Woolfenden, Burgess; Burns (Aluko 86), Bakinson, Morsy (c) (Carroll 21), Thompson; Chaplin, Jackson (Bonne 45+3), Celina
Booked: Thompson, Donacien
Subs not used: Hladky, Vincent-Young, Norwood, Pigott
Pompey (3-4-3): Bazunu; Carter, Raggett, Robertson (c); Romeo, Tunnicliffe, Thompson (Morrell 71), Ogilvie; Curtis, Hirst (Walker 86), O’Brien (Hume 84)
Booked: Thompson, Curtis
Subs not used: Webber, Vincent, Jewitt-White, Mingi
Referee: Christopher Sarginson
Attendance: 25,500 (1,986 Pompey fans)