They went ahead through Aiden O’Brien early in the second half, only for Kieran Sadlier to level from the penalty spot and ensure the spoils would be shared.
Danny Cowley made three changes from the side that drew with Wycombe on home soil 17 days earlier.
Michael Jacobs, Joe Morrell and O’Brien all returned to the starting line-up, with Mahlon Romeo, Ryan Tunnicliffe and Tyler Walker dropping to the bench.
Also among the substitutes was Shaun Williams, who had recovered from the back injury he suffered at the end of January.
The first half was full of bright attacking play from both sides, with plenty of dangerous forays forward at each end of the pitch.
And yet a combination of solid defending and a poor final pass meant that there was little in the way of clear-cut openings.
One neat passage from Pompey saw the ball ping around the box and yet it would not quite fall kindly on a number of occasions.
It was certainly an open contest, although when Marcus Harness met a Jacobs free-kick, he could only guide his header into the arms of James Trafford.
A key interception then prevented the ball from reaching the feet of Harness inside the area following good work from Jacobs and George Hirst.
But it was Bolton who had the best chance to forge ahead before the interval, with Dapo Afolayan looking certain to slot his shot into the bottom corner.
Gavin Bazunu got down to his left to make a superb save, however, and Dion Charles could only blast the loose ball across the face of goal.
The only other incident of note before the whistle blew was a crude Kyle Dempsey challenge on Harness that earned the midfielder a yellow card.
Bolton Wanderers 0
Pompey had not forced Trafford into action before the break, but the keeper was soon picking the ball out of his net after the restart.
It came after Will Aimson – who had only just entered the pitch – was booked for bringing down Hirst outside the box.
The free-kick from Harness slammed into the wall, but the ball was recycled and the same player cut it back for O’BRIEN to slot home.
Wanderers felt that the scorer was offside in the build-up, although he had actually received possession from a white-shirted player.
The visitors might have strengthened their lead moments later and Trafford was relieved to see the ball land safe when he palmed a Sean Raggett header right back into the danger zone.
It was suddenly a frantic affair and after Jon Dadi Bodvarsson’s penalty appeals were rightly waved away, the Blues broke and Hirst drew a save from Trafford.
But the action quickly switched to the other end of the pitch and Bazunu had to beat away a shot from Charles.
Pompey were next to threaten when an O’Brien shot was blocked and George Johnston bravely flung himself into the path of Jacobs’ follow-up.
The hosts had a chance to level on 76 minutes, however, when Elias Kachunga made the most of a challenge from Hayden Carter and referee Marc Edwards pointed to the spot.
Bazunu went the right way – getting down to his left – but the penalty from Sadlier was perfectly placed and nestled in the net.
A double switch was made to provide some fresh energy for the closing stages, with Louis Thompson and Jacobs replaced by Williams and Ronan Curtis.
And loanee Walker also entered the fray in the search for a late Pompey winner, replacing Hirst up front.
There were half-chances for both sides during six minutes of stoppage-time, but neither was able to turn one point into three.
Bolton (3-4-1-2): Trafford; Jones, Santos (c) (Aimson 46), Johns; Sadlier, Morley, Dempsey (Williams 70), Johnston; Afolayan (Kachunga 65); Bodvarsson, Charles
Goals: Sadlier 76 (pen)
Booked: Dempsey, Aimson
Subs not used: Baptiste, Thomason, Amaechi, Bakayoko
Pompey (4-2-2-2): Bazunu; Carter, Raggett, Robertson (c), Ogilvie; Thompson (Williams 82), Morrell; Harness, Jacobs (Curtis 82); O’Brien, Hirst (Walker 85)
Goals: O’Brien 50
Subs not used: Webber, Romeo, Tunnicliffe, Hume
Referee: Marc Edwards
Attendance: 13,809 (700 Pompey fans)