Neymar opened the scoring with a picture-perfect free-kick in the 20th minute, before adding another just two minutes later.
In the 81st minute the former Barcelona star rounded off his treble before being substituted a minute later.
Dating back to August 12, Neymar has now scored or assisted in 12 consecutive games, including two friendlies for Brazil against the USA and El Salvador.
In that 12-game run, Neymar has tallied 12 goals and three assists.
The 26-year-old particularly enjoys home European nights, having now registered seven goals and two assists in just four career Champions League matches with PSG at Parc des Princes.
With his hat-trick on Wednesday, Neymar became the third Brazilian to notch multiple Champions League hat-tricks, joining Luiz Adriano and Adriano in accomplishing the feat.
He also tied his compatriot Kaka for the most goals scored by a Brazilian in the Champions League with his 30th career goal.