When he was snapped up in 2001, chairman Milan Mandaric proclaimed him a 'gift to Pompey fans' and it was quite the shock when he arrived 20 years ago.
This is the tale of a European Cup winner, a chain-smoker, a former Real Madrid and Barcelona star, and probably the only human in existence to ever be annoyed with Linvoy Primus, The Nicest Man In Football™.
Having won the biggest trophy in club football aged 22, it's reasonable to suggest Croatia international Prosinecki will have wondered where it went wrong on February 2, 2002.
A hat-trick against Barnsley was an undoubted high for the 33-year-old midfielder, who dazzled at Fratton Park that day.
His second is a delight, driving forward, foxing a defender with a feint, stumbling, producing a drag back, and then firing in off the post from outside the box with his left foot.
The third? A stunning free-kick with his right foot, which saw him run to the fans, point to badge in glee, before being embraced by Courtney Pitt and a young Peter Crouch. Sadly, it all went sour.
"It was like he was playing them on his own," Primus told FourFourTwo. "He scored a hat-trick and we were 4-2 up with about 10 minutes to go. Then I got sent off - I can't remember what happened, but I'm sure it was harsh - and Barnsley ended up drawing the game 4-4."
Prosinecki would later tell Played Up Pompey: "How I wish the match could have ended there and then, I am sure the fans felt the same, but there were 21 minutes remaining and it didn't turn out that happy for any of us.
"You wonder how you can score three goals and still not win a match? You don't think it is possible, but it happened that day, and in the last seven minutes of the match. Incredible.
"I was a little bit angry afterwards, I admit that, and didn't even ask to keep the match ball. We didn't win so it didn't seem right. I was very annoyed.
"To be 4-2 up and draw 4-4 is football, that is life, but it would be the only hat-trick of my career, the first and last time, and I couldn't celebrate also getting a win. I was not happy!
"I left the dressing room very quickly."
Teammate Gary O'Neil shed more light on exactly how Prosinecki felt that evening.
He told talkSPORT: "In the dressing room after the game he just threw his boots down and looked at us with disgust, like: 'You lot are rubbish. I just scored a hat-trick at home and we still can't even beat Barnsley'.
"And then he went to the kit room with the kit man to have a fag."
After the match, Pompey fan Rick Jackson saw his hero heading home.
"He was angry - you could see it in his eyes," he told The News. "He lit a cigarette and someone bought him a whisky."
Crouch, just 20 when Prosinecki arrived, was a player to benefit hugely, netting 19 goals that season, many assisted by the Croat, earning a move to the Premier League with Aston Villa.
He delighted in what his teammate was able to do on the pitch, despite having seen his career blighted by injuries during his time with Real Madrid and Barcelona.
"Robert fitted the word 'maverick' perfectly and the only time he wasn't smoking a Marlboro Red was when he was on the pitch.
"We would barely see him at training during the week but, my God, when he played for Portsmouth he was unbelievable.
"He had this trick where he would shape to shoot, feint and then roll his foot over the ball to leave the defender absolutely bamboozled.
"You knew it was coming, you could see a mile off what he was going to do, but it was just impossible to stop.
"He must have been some sight in his pomp, when he played for Red Star Belgrade and Real Madrid. He was a one-man band for Portsmouth, a joy to behold."
Prosinecki knew himself he hadn't hit the heights he could well have done in his career, Real lost two consecutive league titles on the final day of the season in 1991/92 and 1992/93, both times with losses to Tenerife.
Coach Benito Floro had even labelled him "another Pele, another Cruyff" in 1992, but his 29 appearances only generated three goals.
The one year Real Madrid did win the title with him on the books he was away on loan with Real Oviedo, although he did at least play in a win against his parent club in that 1994/95 campaign.
In retrospect, though, he found pride in his spell at the Bernabeu: "My time at Madrid could certainly have been better, seeing as people only remember the titles you win," he said.
"I established myself there at a time when foreign players were limited, and I discovered a different type of football, despite injuries and lost titles."
After flirtations with Atletico Madrid, he left Real for rivals Barcelona on a free transfer but injuries held him back under Johan Cruyff, a man Prosinecki greatly admired.
Injuries struck again though, and within a year and a half he was sold to Sevilla, beginning his descent from the top.
Prosinecki isn't bitter about his lack of success at two global powerhouses, he insists: "All players dream of playing for Real or Barça - I played for both of them! And I have wonderful memories of it all.
"Above all, I feel as if I left the people there with good memories of me. I don't think there are that many players who have worn both shirts and left good impressions at both clubs.
"These days, when I see the welcome I get at both Madrid and Barcelona, it makes me think that my time at the clubs can't have been completely wasted."
After spells in Croatia and Belgium, he found himself at Fratton Park, despite good displays at the 1998 World Cup, where he scored twice.
It was an odd journey, and even his new teammates couldn't quite believe what was happening.
Could an injury-prone skilful superstar really hack it in the First Division? He let his feet do the talking, that much is sure.
"He was ancient when he came to play for us, but he was still brilliant," O'Neil told talkSPORT.
"When he came to the club I thought: 'He's rubbish! He cant run, how's he going to play for us?' But he'd get the ball and you were just like: 'Oh my God, this guy is a genius!'
"You couldn't get the ball off him, he'd do step overs that would fool an entire team.
"He literally couldn't run, it was like playing football with your Dad!
"But he was an unbelievable player. He trained at a tempo he wanted to train at, he'd just play in the number ten and I would do all his running, but he was breath-taking. The stuff he did was incredible."
Portsmouth fans aren't in any hurry to forget the season a European Cup winner enraptured them.
They actually finished the campaign in 17th position and almost exactly like his time at Real Madrid, success would come as soon as he left.
In the very next season, Harry Redknapp helped them earn promotion to the Premier League, Arsenal legend Paul Merson took Prosinecki's role as mercurial midfielder.
The reality though, is he left a much bigger legacy to those who ventured to Fratton Park.
He was their skilful, chain-smoking, superstar, and will always be considered a club legend.
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