Ben Thompson’s stunning strike gave them the lead, only for Paddy Madden and a Ched Evans penalty to see the hosts ahead at the break.
But Dean Marney’s red card for two bookable offences proved crucial – and the Blues took advantage.
Brett Pitman levelled with another spot-kick and a first goal of the season from Anton Walkes ensured they retook the lead.
It was left to Jamal Lowe to wrap things up with a brace that ensures Pompey will welcome in 2019 at the top of the table.
Kenny Jackett made three changes from the side that suffered a first defeat on the road at Gillingham on Boxing Day.
Two of them were enforced, with Walkes and skipper Pitman replacing Nathan Thompson (hamstring) and Oli Hawkins (ankle) respectively.
The other switch came in the middle of the park, where former Fleetwood star Gareth Evans made way for Ben Close.
That meant a switch to a 4-3-3 system, with Lowe and Ronan Curtis flanking Pitman in the forward line.
The hosts had a great opportunity in the opening stages, but Evans’ header was held low down to his left by Craig MacGillivray.
Pompey soon started to settle and Close was unable to make a clean connection with his shot, allowing Alex Cairns to save.
But the Cod Army keeper made an even better stop soon after, keeping out a volleyed effort from Matt Clarke after the defender’s first attempt had been blocked.
The visitors then received a blow when Lee Brown went down injured and had to come off, with Brandon Haunstrup replacing him at left-back.
There was reason to celebrate for the travelling supporters on 26 minutes, however, as their side took the lead.
It was a fine finish from THOMPSON, whose fierce effort from outside the box struck the underside of the crossbar and bounced down over the line.
Close might have doubled the lead, but could not get enough power on his header from a Lowe cross to trouble Cairns.
Instead it was Fleetwood who were next to score on 39 minutes, when Madden raced in to meet Lewie Coyle’s cut-back and arrow a first time shot right into the bottom corner.
And it soon got even worse for the Blues as Madden fired past the post, but went down after colliding with Clarke and, following a lengthy pause, referee Matt Donohue pointed to the spot.
It was Evans who stepped up to take the penalty, sending MacGillivray the wrong way to turn the contest on its head.
Pompey might have levelled deep into stoppage-time, only for Ross Wallace to clear behind and prevent Lowe from converting Curtis’ delivery at the back post.
Fleetwood Town 2
The Blues were quickly out of the traps following the interval, but when a corner was cleared, Haunstrup fired wildly off target.
Hopes were raised soon after, though, when Marney fouled Thompson and – having earlier been booked for a challenge on Curtis – saw red.
A cross from Haunstrup was then hacked to safety, as Walkes raced into the box to try to make contact.
Jackett soon made an attacking switch, with Evans brought on to provide more of a goal threat and Close withdrawn.
But it was two other players who provided the drama that saw the Blues score twice in as many minutes to take the lead.
Donohue pointed to the spot for the second time after Curtis was brought down by Ross Wallace and PITMAN confidently slammed home the spot-kick.
It soon got even better, though, as the Cod Army failed to deal with a Curtis cross and WALKES bent a shot into the top corner with his left foot.
The action did not stop there, however, and MacGillivray kept out Wes Burns’ free-kick, then quickly recovered to keep out James Wallace’s follow-up effort.
There was a period of calm after that, although Pompey were not content to sit back and Curtis continued to torment the home defence.
But they were lucky to still be ahead when, following a Fleetwood corner, both Madden and James Wallace struck the post.
Tom Naylor then hacked the ball clear from the line before Pompey went up the other end to wrap things up.
LOWE collected a pass from Curtis and held off two challenges, turning neatly to sneak a low shot inside the near post.
And it soon got even better for the Blues, as LOWE raced on to Thompson’s fine pass and lashed home their fifth goal of an eventful afternoon.
Andre Green came on for Curtis in the closing stages, but the visitors were unable to grant the wishes of the travelling fans, who chanted ‘we want six’.
Clarke came closest to adding another, but his header was well saved by Cairns. It mattered not, as Pompey had done more than enough to ensure they would end the year at the summit.
Fleetwood (4-4-2): Cairns; Coyle, Morgan (c), Eastham, R.Wallace; Burns (Dempsey 63), Marney, Biggins (Bolger 79), Hunter (J.Wallace 54); Madden, Evans
Goals: Madden 39, Evans 43 (pen)
Sent off: Marney (two yellow cards)
Subs not used: Jones, Sheron, Holt, McAleny,
Pompey (4-3-3): MacGillivray; Walkes, Whatmough, Clarke, Brown (Haunstrup 19); B.Thompson, Naylor, Close (Evans 53); Lowe, Pitman (c), Curtis (Green 90)
Goals: Thompson 26, Pitman 57 (pen), Walkes 58, Lowe 81, 84
Subs not used: Bass, Burgess, Wheeler, Mason
Referee: Matt Donohue
Attendance: 3,494 (853 Pompey fans)