The summer signing netted in each half, as the visitors appeared to be cruising towards three points at a grey Bloomfield Road.
Mark Cullen’s late effort meant the ending was perhaps nervier than it might have been and the same player also had a goal disallowed, as the Blues held on for what was a deserved win.
Kenny Jackett made three changes from the side that beat Luton on home soil on the opening day.
With Brett Pitman on the bench, Gareth Evans skippered the side and lined up alongside Ben Close in a 4-1-4-1 system.
Oli Hawkins was handed the striking role, as Brandon Haunstrup and the injured Nathan Thompson made way.
The stands were sparsely populated in all but the away end, as the Seasiders support staged protests against their club’s owners outside the ground.
But those who had made their way through the turnstiles almost witnessed a goal in the opening seconds, with Joe Dodoo striking the post from a narrow angle.
The danger was not over for the visitors, however, as Nathan Delfouneso’s follow-up effort had to be blocked by Matt Clarke.
A promising spell of possession soon led to a chance at the other end and an Evans cross was headed narrowly wide by Hawkins.
But the deadlock was broken on nine minutes and it was a moment to remember for CURTIS as he opened his Blues account.
The Blackpool defence failed to deal with Hawkins’ header, allowing the summer signing to pick the ball up and force it home, with Mark Howard’s hand not forceful enough to divert it wide.
Pompey were in control and looking more likely to add to the scoring as the half progressed, although there were not an abundance of clear-cut opportunities.
Curtis and Hawkins both glanced wide from dangerous deliveries into the box, while a tightly-marked Jamal Lowe was unable to get a shot away following good work from Close.
The Blues started to look more dangerous as the interval approached, though, and Howard was forced into action to deny Curtis.
Evans then whipped in a free-kick from wide on the left that a stretching Hawkins was inches away from connecting with.
It had been a quiet start for Craig MacGillivray and he was not overly troubled by Chris Taylor’s attempt from a tight angle.
Curtis went much closer on 38 minutes, surging through the centre of the pitch and unleashing a strike from outside the box that crashed against the post.
There were a couple of half-chances for the hosts before the whistle, although nothing to overly trouble MacGillivray.
Blackpool had been poor before the break, but did look more assured following the restart, albeit without creating much.
The town’s air show was causing more of a nuisance, with hair-raising stunts overhead meaning it was often difficult to focus on what was happening on the pitch.
There was a booking for Evans for clattering into Taylor, while the midfielder then saw his free-kick nodded wide by Curtis.
The hosts did have a decent opening just before the hour mark, although Delfouneso could not convert Marc Bola’s low cross as he slid in.
Instead Pompey went straight back up the other end to double their advantage after a long ball had been headed on by Hawkins.
It was CURTIS who picked the ball up, advancing on goal and neatly slotting it through the legs of Howard.
There was more good news when Danny Rose replaced Close on 66 minutes, with the midfielder making his first competitive appearance since suffering a leg break at the end of December.
MacGillivray had a couple of comfortable saves to make as Blackpool tried to find a way back, while Joe Bunney drilled narrowly wide.
But the Blues did not look under too much threat and David Wheeler was introduced for his debut, with Lowe the player to make way.
Blackpool did have a goal on 81 minutes, though, and it came just seconds after Evans had volleyed narrowly over.
The ball was pumped up the pitch and went straight into the path of substitute Cullen, who lifted it home under pressure from Clarke.
Taylor and John O’Sullivan both had chances as the seconds ticked down, while Cullen did find the net again – only for his celebrations to be cut short by the linesman’s flag.
It was a heart-stopping moment for those travelling fans in the North Stand, but the final whistle came moments later to spark jubilant scenes.
Blackpool (4-3-3): Howard; Turton, Heneghan, O’Connor, Bola (Gnanduillett 72); Taylor, Spearing (c), Pritchard (O’Sullivan 60); Delfouneso, Dodoo (Cullen 60), Bunney
Goals: Cullen 81
Subs not used: Mafoumbi, Nottingham, Thompson, Sinclair-Smith
Pompey (4-1-4-1): MacGillivray; Walkes, Whatmough, Clarke, Brown; Naylor; Lowe (Wheeler 79), Evans (c), Close (Rose 66), Curtis; Hawkins
Goals: Curtis 9, 59
Booked: Evans, Naylor
Subs not used: McGee, Burgess, Haunstrup, Dennis, Pitman
Referee: Ross Joyce
Attendance: 4,154 (1,638 Pompey fans)