Pompey had to be content with a point at Bloomfield Road after Blackpool survived playing more than half the game with just 10 men.
Jordan Rhodes was sent off shortly before the break, with Abu Kamara and substitute Kusini Yengi both striking the woodwork.
But despite committing plenty of men forward for the contest’s closing stages, the Blues were not able to find a goal.
John Mousinho made a single change from the side that beat Oxford on home soil the previous weekend.
It came at left-back, where an injury to Connor Ogilvie saw Jack Sparkes restored to the starting line-up.
That opened up a place on the bench that was filled by Zak Swanson following his recovery from a groin problem.
Both sets of fans made plenty of noise as the action got started and their respective teams responded by looking to get forward.
That attacking intent was not being converted into clear-cut openings, however, with the game turning into a bitty affair.
But it was the hosts who settled quicker and they began to apply some pressure on the Blues back-line.
Hayden Coulson dragged the ball past the post, while a brilliant Joe Rafferty challenge stopped Jake Beesley getting a shot away.
And when Karamoko Dembélé swung in the resulting corner, Rhodes could only nod it wide at the back post.
Pompey were able to calm things down as the interval approached, though, showcasing some patient passing football.
And they had a numerical advantage when Rhodes led with his arm in an aerial challenge with Rafferty and was, perhaps harshly, shown a red card by referee Ed Duckworth.
The Blues almost made the most of that in stoppage-time, when Paddy Lane was tackled and the ball ran towards Kamara.
He hit a low shot towards the goal, but Dan Grimshaw used his fingertips to turn it against the inside of the post.
Half Time: Blackpool 0 Pompey 0
There was a change for the visitors at the break, with Myles Peart-Harris – who had been booked – replaced by Owen Moxon.
Pompey looked to get at their opponents, but Sparkes could not convert a Rafferty cross at the back post and received a harsh booking for his troubles.
Lane then collected a threaded Conor Shaughnessy pass on 55 minutes and hit a long-range effort that was blocked.
Callum Lang had been on the end of a heavy challenge earlier in the half and tried to play on, but was eventually replaced by Christian Saydee.
Last weekend’s goal hero immediately made an impact, surging forward and laying the ball off for Kamara.
But the winger’s shot was blocked and Saydee did well to get in a follow-up attempt that was hacked to safety.
A long ball up the pitch from Colby Bishop was then nodded back by Jordan Gabriel, but the header was not the strongest and Grimshaw only just got to it before Lane.
Pompey were probing, but struggling to find a way through the Seasiders, who were getting plenty of men behind the ball.
They did have an opportunity when Lane was brought down on the edge of the box, but Grimshaw kept out the free-kick from Sparkes.
Mousinho made an attacking switch on 74 minutes, with Sparkes making way to be replaced by Yengi.
They kept looking for a breakthrough and Kamara did brilliantly to cut inside from the right before finding Moxon to hit a low shot that was saved by Grimshaw.
And when the ball ran kindly for Yengi, he then burst into the box and hit a shot that Grimshaw turned against the post.
Pompey kept pushing and Kamara’s deflected cross hit the post and just evaded Moxon at the back post, while neither Bishop or Yengi could quite connect with a Saydee delivery moments later.
They almost found a goal in stoppage-time, but Lane’s low drive was parried by Grimshaw and defender Marvin Ekpiteta was first to the loose ball to ensure Blackpool claimed a point.
Blackpool (3-4-3): Grimshaw; Pennington, Ekpiteta, Husband (Casey 19); Gabriel, Byers, Norburn (c), Coulson; Dembélé, Rhodes, Beesley (Joseph 78)
Sent off: Rhodes
Booked: Norburn
Subs not used: O’Donnell, Carey, Virtue, Hamilton, Lavery
Pompey (4-2-3-1): Norris; Rafferty, Raggett, Shaughnessy, Sparkes (Yengi 74); Pack (c), Peart-Harris (Moxon 46); Kamara, Lang (Saydee 56), Lane; Bishop
Booked: Peart-Harris, Sparkes, Moxon, Saydee
Subs not used: Macey, Swanson, Towler, Martin
Referee: Ed Duckworth
Attendance: 11,811 (2,115 Pompey fans)
