Arizona went up in a 2-0 lead in the first period, but before the period was over the LA Kings had time to reduce through Jaret Anderson-Dolan.
In the second period, the evening's first Swedish goal came when Johan Larsson led 3-1 for Arizona and then it looked tough for the Kings.
But in the third period, they grabbed the match and turned the tables.
Stjärnbacken Drew Doughty played great and the Swedes scored.
First, Adrian Kempe put 3-2 after good interaction with Kale Clague, then Jeff Carter equalized and with just over six minutes left to play, Carl Grundström was the one who finally steered in Doughty's shot from the blue line.
The goal was 23-year-old Grundström's fifth in the NHL this season.
The Los Angeles Kings are still second to last in the Western Division, while Arizona actually has the final playoff spot right now.