The Stockholm team got a dream start in the Coop Norrbotten arena when Alice Östensson gave Djurgården the lead after just 24 seconds.
Before the first period was completed, Luleå had a receipt through only 16-year-old Wilma Sjölund, her first goal in the Swedish women's hockey league, but at the beginning of the middle period the away team was back in leadership.
Djurgården's Sarah Bujold took the puck in front of goal before Luleå's goalkeeper Sara Grahn failed to knock it off - and instead pulled the puck into her own net.
For Luleå, the loss was the third of the season in eight games.