The visitors were not exactly sparkling, not that there would be much concern from them as they headed back north with three points in the bag.
Sloppy defending cost the Blues once more, with Kyle Vassell and Clark Robertson taking advantage to find the net.
Kenny Jackett unsurprisingly stuck with the same side that secured victory at Fleetwood earlier in the week.
That meant Matt Clarke continued to wear the captain’s armband in Brett Pitman’s absence, while a fit-again Kal Naismith had to be content with a place on the bench.
The first half was an instantly forgettable affair, with both sides guilty of a lack of quality and a poor range of passing.
It was not without chances, though, and Vassell dragged a shot past the post after Conor Chaplin had lost possession in the centre.
Jamal Lowe whipped in a decent cross at the other end of the pitch, but a diving Oli Hawkins could not quite make a connection.
He did get on the end of another Lowe delivery on 15 minutes, although this time the ball was diverted over.
The striker was left punching the turf after going down injured soon after, but was thankfully able to run it off.
Blackpool then had a chance from a Jay Spearing corner that centre-back Robertson glanced past the post.
Lowe had earlier been booked for kicking the ball away, although Vassell somehow escaped the same punishment for a blatant off-the-ball trip on Christian Burgess.
Hawkins should at least have tested Seasiders keeper Joe Lumley on 31 minutes, only to hook wide when Dion Donohue’s deep free-kick was headed down by Clarke.
Vasell was more clinical just before the interval, however, calmly slotting the ball home after stealing possession from Burgess.
Anyone expecting an increase in entertainment following the interval was in for a disappointment, as the action continued to meander along.
That was no concern for Blackpool, though, who were more than happy to protect their slender lead.
A promising move involving Lowe and Anton Walkes eventually broke down just inside the visitors’ box, while Clarke slid on to deny Jimmy Ryan at the other end.
Jackett made his first switch just before the hour mark, with Kennedy withdrawn for the fresh legs of Connor Ronan.
With things not improving a second change soon followed, as Naismith was brought on for Hawkins, who still appeared to be affected by his earlier knock.
But it soon got worse for the Blues, with Ronan’s clearance only finding Jay Spearing, whose cross from the right was nodded home from close range by an unmarked Robertson.
A late fightback was not really looking on the cards and it might have got worse, with Curtis Tilt only able to head Ryan’s centre straight into Luke McGee’s arms.
Plenty of fans took an opportunity to beat the traffic, with a steady stream heading for the exits as the minutes ticked away.
But they did not miss much, as the only cheers were of the ironic variety when Pompey finally had a late shot on target.
Pompey (4-4-2): McGee; Walkes, Burgess, Clarke (c), Donohue; Lowe, May, Close, Kennedy (Ronan 56); Chaplin, Hawkins (Naismith 61)
Subs not used: Bass, Whatmough, Haunstrup, Deslandes, Smith
Blackpool (4-2-3-1): Lumley; Turton, Tilt, Robertson, Daniel (Taylor 90+2); Spearing, Ryan (c); Mellor, Delfouneso, Solomon-Otabor (Philliskirk 68); Vassell (Gnanduillet 83)
Goals: Vassell 41, Robertson 63
Subs not used: Mafoumbi, Aimson, D’Almeida, Agyei
Referee: Gavin Ward
Attendance: 17,895 (264 away fans)