The former PSG right-back was highly rumoured to join Manchester United but North London rivals Spurs brought in the right back after Kyle Walker left for Manchester City.
Although Neymar did not add to his three goals, his free kick led to PSG's second goal, which was scored by midfielder Thiago Motta.
Neymar was "stunned" by the legal action Barcelona had taken against him and confirmed he would seek the second payment be made by the club.
Barcelona said on Tuesday that they want Neymar to pay back the bonus for a contract in October 2016 that tied him to the club through 2021. They also want an additional 10 percent interest.
Brazilian striker Neymar scored twice as PSG routed Toulouse 6-2 in French league.
Since joining in July 2011, Matuidi has played 295 games for Paris Saint-Germain, seventh overall in the club's history, scoring 33 goals and dishing out 30 assists.
Suarez will now miss Barca's first four league matches of the season, against Betis, Alaves, Espanyol and Getafe and presumably their Champions League debut.
Neymar looked intensely focused from the start, easily switching from one wing to the other, and often taking a playmaker role.
PSG wanted Neymar to start the season at the Parc des Princes but his debut was delayed because of the paperwork issues.
PSG said Neymar would have been included in the squad if the document had been submitted in time. The former Barcelona star had said he was ready to play during his first press conference in Paris.
The Brazilian will wear the No.10 shirt for the Ligue 1 outfit after Argentinian playmaker Javier Pastore volunteered to relinquish the number for his new teammate.
The Brazilian star flew in from Barcelona on a private jet for his official presentation, arriving in a city whose soccer fortunes he is expected to transform.
Paris Saint-Germain ended weeks of speculation by paying Barcelona the 222 million-euro ($264 million) release fee written into Neymar's contract with the Catalan club.
Neymar completed his blockbuster transfer from Barcelona to PSG for 222 million euros (262 million US dollars) on Thursday.
To secure the services of Neymar, PSG splashed 222 million euros - double the previous world record transfer of 105 million euros paid last year by Manchester United for France midfielder Paul Pogba.
Neymar is poised to become an even better player in Paris than the one who has dazzled Camp Nou with his lightning-quick feet and flair for beautiful goals.
The payment of the clause shatters the previous world record transfer of 105 million euros (then $116 million) that Manchester United paid for France midfielder Paul Pogba last year.
French President Emmanuel Macron met with PSG President Nasser al-Khelaifi on the sidelines of a charity event Thursday, and told him "congratulations, I understand there's been some good news."
Neymar is expected in Paris in the coming days.
The son of a journeyman soccer player for Brazil's smallest teams, Neymar was born in the industrial city of Mogi das Cruzes, some 60 kilometers north of Sao Paulo, the country's biggest metropolis.
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