Her title-clinching double 18 in the final leg condemned Hedman to a third defeat in a world final.
Gulliver said: “I’m absolutely delighted. It was always going to be a tough game against Deta. She wanted her first (title) and I wanted my 10th, so it was always going to be a battle.
“I’ve got the fire in my belly again. It all started in 2001 and we’re here again. Ladies darts is getting stronger and stronger and stronger.”