In Napoli's commanding 3–0 victory over Fiorentina on 17 February 2012, Lavezzi rounded off the scoring in the 90th minute with a long-range goal. Four days later, he scored his first two Champions League goals; they came in a 3–1 first leg victory over Chelsea in the Round of 16. The following Sunday, on 26 February, Lavezzi scored the only goal of the game as Napoli defeated Internazionale and climbed up to fifth place in the Serie A standings.
Lavezzi popped up in the 86th minute to score the winning goal against Parma on 4 March 2012, though the result was controversial, as Lavezzi appeared to be in an offside position. Lavezzi netted a penalty and provided an assist as Napoli tore apart Cagliari 6–3 on 9 March to warm up for their Round of 16 second leg tie against Chelsea. Lavezzi scored his ninth and final Serie A goal of the season in a 3–1 loss to Atalanta on 11 April after receiving the ball from Goran Pandev and pushing it past goalkeeper Andrea Consigli.
Lavezzi won his first piece of silverware with Napoli on 20 May 2012 as the club defeated Juventus 2–0 in the Coppa Italia final. During the match, Lavezzi was fouled in the penalty box by Juventus goalkeeper Marco Storari, and Napoli were awarded a penalty, which Edinson Cavani dispatched to give Napoli their first goal and set the club on their way to their first trophy in more than 20 years.
On 2 July 2012, Ligue 1 club Paris Saint-Germain confirmed that they had agreed with Napoli to a €26.5 million transfer fee for the rights to Lavezzi and signed him to a four-year deal, reportedly worth up to €30 million. On 11 August, Lavezzi made his PSG debut against FC Lorient in a 2–2 draw in the opening match of the 2012–13 Ligue 1 season. His first two goals for PSG came on 21 November in the Champions League, securing qualification to the Round of 16 with a 0–2 away victory over Dynamo Kyiv.