In truth, neither side deserved to win a dire contest that did little to entertain another large travelling army.
But it was the Shakers who were able to celebrate the consolation of three points, as George Miller stole the ball from Luke McGee to score.
Kenny Jackett made four changes from the side that were beaten at home by Charlton the previous week.
Oli Hawkins returned up front and Connor Ronan started wide on the left in a 4-4-2 system, while there were also places for Stuart O’Keefe and Christian Burgess.
Gareth Evans and Brandon Haunstrup both dropped to the bench, as Jack Whatmough missed out through injury and Kal Naismith was not included in the squad.
The first half was an instantly forgettable affair, with little in the way of goalmouth action at either end of the pitch.
It was typical end-of-season fare, as both sides displayed plenty of energy, but not much quality in the final third.
Ben Close fizzed a dangerous delivery across the face of goal, although none of his team-mates were there to get on the end of it.
Bury were mildly more threatening and Harry Bunn had an angled effort that cleared the crossbar.
Jay O’Shea then turned sharply inside the Blues box and hooked the ball narrowly over, in what was probably the best chance of the half.
Hawkins should have fond the target when he dived to meet Jamal Lowe’s cross on 24 minutes, although his blushes were spared by the linesman’s flag.
The hosts were then forced into a change when Bunn went down off the ball and was replaced by Tsun Dai.
Pompey started to find a bit more fluidity just before the break, although Brett Pitman and Lowe were both unable to find the target.
Any hope that the second half was going to be livelier than the first appeared to be dashed when O’Shea failed to beat the first man with a dangerous free-kick straight after the restart.
But the Blues went closer moments later, with Hawkins meeting Lowe’s cross and sending a header looping onto the roof of the net.
There was then a nervy moment for the hosts when Miller caught Matt Clarke with a flailing arm, although referee Andy Haines opted to brandish only a yellow card.
Jackett made his first change on 55 minutes, with Hawkins withdrawn for Matty Kennedy, resulting in a switch back to a 4-1-4-1 system.
A series of corners caused problems for the Shakers, as O’Keefe and Pitman both had efforts deflected off target, while Burgess then headed over.
Another set of fresh legs was introduced just past the hour mark, with Dion Donohue making way for Haunstrup.
Bury almost broke the deadlock soon after following an almighty scramble in the box, but a well-placed Pitman was able to hack Miller’s effort from the line.
It was only a brief reprieve for the Blues, however, as Miller did open the scoring for the hosts on 67 minutes.
But it was a goal that should have been avoided, as Kennedy passed back to McGee and when he took a touch, the Shakers striker nipped in to steal the ball and slot it home.
Kennedy went down under pressure from Ryan Cooney as Pompey sought to get back on level terms, only for appeals for a penalty to be waved away by Haines.
Bury missed a good opportunity to double their lead, however, when Saul Shotton fired over after McGee had punched clear a corner.
Conor Chaplin replaced Ronan for the final few moments and saw a stoppage-time shot brilliant pushed past the post by Joe Murphy.
Burgess then saw his header cleared from the line from the resulting corner, as the Blues were unable to force a late equaliser.
Bury (4-4-1-1): Murphy; Cooney (Clarke 80), Shotton, Thopson, Leigh; Ismail, Danns (c), Styles, Bunn (Dai 33); O’Shea; Miller (Sang 90+2)
Goals: Miller 67
Subs not used: Ripley, Tutte, Adams, Hulme
Pompey (4-4-2): McGee; Thompson, Burgess, Clarke, Donohue (Haunstrup 63); Lowe, Close, O’Keefe, Ronan (Chaplin 85); Pitman (c), Hawkins (Kennedy 55)
Booked: Thompson, Donohue
Subs not used: Bass, Deslandes, May, Evans
Referee: Andy Haines
Attendance: 4,575 (1,525 Pompey fans)