The Brazil international trebled the team's advantage on the stroke of half time after Gerard Pique and Pedro had fired the hosts into the lead, before bagging a further two goals to register his first strikes in Europe's premier competition.
Gerardo Martino's men had slumped to back-to-back defeats against Ajax and Atletic Bilbao in recent fixtures, and Neymar is thrilled that his contribution helped provide the tonic to those losses.
Speaking to Marca, the 21-year-old said: "I'm very happy - not only for the three goals in the Champions League, but also for the team's win.
"I did not feel the pressure, but I wanted to make my mark. The important thing is we were able to overcome those two losses and now we must change our mindset to think about La Liga. "
Christian Tello added gloss to the scoreline later on, before Georgios Samaras hit a consolation in the dying stages.
Consequently, Barca finish up as Group H winners, with AC Milan finishing second ahead of Monday's draw for the last-16 stage in Nyon.