The hosts controlled possession, but aside from a Rasmus Nicolaisen effort that was cleared from the line, rarely threatened to score.
It was equally uneventful at the other end of the pitch, but Jerry Yates found the target in the closing stages to ensure the Blues’ promotion bid stuttered again.
There were two changes from the side that were beaten on the road against Bristol Rovers earlier in the week.
Marcus Harness and Nicolaisen both came into the starting line-up, with George Byers dropping to the bench and James Bolton missing out with a knock.
Much like the reverse fixture earlier in the season, the first half was extremely short on clear-cut opportunities.
But there was almost an early opener for the visitors after Craig MacGillivray got down to parry clear Ellis Simms’ angled drive.
The ball ran did not run safe, though, and with Yates about to tuck it away, Charlie Daniels slid in to make a crucial block.
Nicolaisen then tried to reach a corner from the left-back at the other end of the pitch, but was only able to nod wide.
The visitors were unhappy with some of the decisions from the referee, with Luke Garbutt particularly aggrieved to be shown a yellow card following a late challenge on Ronan Curtis.
Pompey were growing into the contest and were left wondering how they failed to take the lead on 29 minutes.
Curtis swung a free-kick into the box from wide on the right and Harness’ first time effort was blocked by Garbutt.
But he was able to collect the loose ball and tee-up Nicolaisen, whose goal-bound effort was cleared from the line by James Husband.
It was the Blues looking the more likely to break the deadlock as the interval approached, although the final pass was lacking.
Sean Raggett was not quite able to make a clean contact with an ambitious over-head effort, while a dangerous Ryan Williams delivery would not land for a team-mate.
The game failed to explode into life after the restart, with Pompey seeing plenty of the ball, but unable to break through the Blackpool back-line.
Neither side were providing much of an attacking threat, with the underworked keepers probably glad that it was a fairly mild February afternoon.
The first change arrived just past the hour mark, with Byers on for Harness to provide the hosts with some fresh impetus.
Curtis sent a decent cross into the box soon after, but it was Husband who got there first to head clear.
But for all of the possession the Blues were having, they were not able to find a path through to Maxwell’s goal.
A double switch arrived in an attempt to change that on 77 minutes, with John Marquis and Williams replaced by Ellis Harrison and Jordy Hiwula.
Blackpool had not caused any problems, but launched a quick break moments later and MacGillivray dived to his right to parry clear Elliot Embleton’s curler.
The danger was not over, however, and the keeper recovered swiftly to also repel the follow-up attempt from Garbutt.
But he could not stop Yates from breaking the deadlock on 82 minutes, with the striker running half the length of the pitch, side-stepping a challenge and drilling a shot into the bottom corner.
Blackpool tried to use up as much time as possible as the seconds ticked down and Pompey were unable to find an equaliser.
Pompey (4-4-1-1): MacGillivray; Johnson, Raggett, Nicolaisen, Daniels; Curtis, Naylor (c), Cannon, Harness (Byers 61); Williams (Hiwula 77); Marquis (Harrison 77)
Booked: Cannon, Curtis
Subs not used: Ward, Whatmough, Brown, White
Blackpool (4-4-2): Maxwell (c); Gabriel, Ballard, Husband, Garbutt; Ward (Virtue 85), Stewart, Dougall, Kaikai (Embleton 75); Simms (Mitchell 46), Yates
Goals: Yates 82
Booked: Garbutt, Simms, Gabriel
Subs not used: Sims, Turton, Thorniley, Lubala
Referee: Sam Allison