They conceded a sloppy opener to Barrie McKay, but Sean Raggett nodded the hosts back on level terms before the break.
Harry Souttar then turned the ball into his own net, with the Cod Army defender soon making amends by securing them a point.
Kenny Jackett made three changes from the side that were beaten on the road at Peterborough at the weekend.
Ellis Harrison missed that game after becoming a father for the first time, but was back to lead the line.
There were also returns for Ross McCrorie and Andy Cannon, as John Marquis dropped to the bench, while Jack Whatmough and the injured Ben Close missed out completely.
Pompey were first to threaten when the ball broke for Ronan Curtis in the box and, from a tight angle, he sent a shot dipping over the crossbar.
But it was relatively slow start to the contest, with a scything Glenn Whelan challenge on Ryan Williams the main point of focus, earning the midfielder a yellow card.
Fleetwood then capitalised on some sloppy play from the hosts to break the deadlock on 19 minutes.
Ched Evans cut the ball back for McKay and his first attempt was saved by Alex Bass, only for the keeper to get into a tangle with Steve Seddon.
It was McKay who was quickest to the loose ball and was able to force it home from a couple of yards out.
The same player then curled a teasing corner into the box and Tom Naylor was forced to head narrowly past his own post.
Fleetwood were looking more likely to add to the scoring and Jack Sowerby’s effort took a deflection, with Bass adjusting well to save.
Pompey finally began to move through the gears, with Harrison forcing Alex Cairns to drop a cross and have to grasp the ball at the second attempt.
And an equaliser did arrive on 36 minutes, when McCrorie’s fine delivery from deep on the right was met by RAGGETT, whose header looped over Cairns and into the net.
Lewis Gibson was booked late in the first half for a terrible dive in the box that, which – for some reason – peeved the Cod Army bench.
They were almost celebrating in stoppage-time, though, as Josh Morris curled a fine free-kick against the post.
Fleetwood Town 1
The hosts were caught napping immediately following the restart and Morris’ centre was pushed out by Bass, with Cameron McGeehan on hand to clear the danger.
But the Blues took the lead moments later, thanks to a searing burst of pace from Williams down the right.
He surged past Lewis Gibson to get on the end of Cannon’s pass and sent in a low delivery that was thundered into his own net by SOUTTAR.
Both sides were looking capable of adding to the scoring, although Harrison scuffed wide after being played through by Curtis.
The Cod Army then broke quickly up the pitch and Morris was left with just Bass to beat, with the keeper coming off his line to make a crucial save.
But the visitors were level on 55 minutes, as Souttar atoned for his earlier indiscretion by nodding home when a corner was headed back across goal by Evans.
Jackett made a double switch to try to regain the advantage, as Williams and McGeehan made way for Marcus Harness and Marquis.
The action continued to swing from one end to the next and Curtis could only nod wide at the back post after meeting a fine cross from Harness.
But there was generally a lack of quality from both sides in the final third, with a point enough to move the Blues up two places fourth.
Pompey (4-2-3-1): Bass; McCrorie, Bolton, Raggett, Seddon; McGeehan (Marquis 65), Naylor (c); Williams (Harness 65), Cannon, Curtis; Harrison
Goals: Raggett 36, Souttar 48 (og)
Booked: Curtis, Harrison
Subs not used: MacGillivray, Downing, Brown, Evans, Hawkins
Fleetwood (3-4-3): Cairns; Connolly, Souttar, Gibson; Coyle, Sowerby (Coutts 69), Whelan, Andrew (Burns 54); Morris (Madden 75), Evans (c), McKay
Goals: McKay 19, Souttar 55
Booked: Whelan, Gibson, Connolly, McKay
Subs not used: Crellin, Thorvaldsson, Biggins, Saunders
Referee: Darren Drysdale
Attendance: 16,775 (64 away fans)