The defender scored three goals in the second half as Paris Saint-Germain cruised to a dominant 5-0 win over the Belgian champions, locking down a spot in the knockout stage.
The efforts were Kurzawa's first for PSG in European competition as well as his first treble for the club.
The hat-trick is nice enough, but Kurzawa also became the first defender in modern Champions League history to achieve the feat in the competition.
He is the second PSG player to score a hat-trick in the Champions League, with Zlatan Ibrahimovic first managing it in October 2013.
The victims that evening were also Anderlecht, who likely want no part of PSG in any European competition in the near future.
Then again, they may not be alone these days as PSG have now scored 17 goals without conceding in the group stage of this year's competition.