18-year-old Yasin Ayari headed in 1-0 on Vincent Thill's inbound corner in the 13th minute.
The AIK talent's third goal of the season.
Then it took until the 36th minute before Nicolas Stefanelli scored the second.
It was a delicious goal, not least it was Nabil Bahoui's heel pass on a touch that stood out.
Two minutes later, it was Bahoui himself who lobbed in 3-0 behind Oskar Jansson in Norrköping's goal.
Norrköping has only one win in the last ten games.
However, they got a way into the match when Vincent Thill was shown a straight red card just before half-time.