Hunt led after the initial two rounds on Friday and was clear after the penultimate dive on Sunday.
However, the 32-year-old over-rotated the entry of his final routine to drop out of medal contention.
Steve LoBue of the United States won gold ahead of Czech Michal Navratil and Italy's Alessandro de Rose.
Hunt's final routine - three forward somersaults and four and a half twists - carried the competition's highest degree of difficulty score of 5.6.
"I was annoyed throwing away the gold medal but I didn't want to be seen as this unbeatable machine," he told BBC Sport.
"This gives me plenty to work on."
Hunt had won medals at each of the previous World Aquatics Championships to feature high diving - claiming silver in the sport's debut at Barcelona 2013 before taking gold at Kazan 2015.
Fellow Briton Blake Aldridge - who dived alongside Tom Daley in the synchronised 10m platform event at the Beijing Olympics in 2008 - finished ninth.
The 34-year-old had been fifth and just 12 points from the podium places heading into the last round, but mistimed his entry.
"I feel completely numb," he told BBC Sport. "To have a chance and completely throw it away on the last dive is heartbreaking."
Aldridge endured a torrid 2016, landing on his back at an event in Dubai and had further injury problems after attempting the then most difficult dive in the world - reverse double with five twists.
"This year has been about getting my confidence back because I landed on my back in Dubai and was coughing up blood for a few days, and then I nearly bit through my tongue at another event," he added.
"I'm currently struggling with an abductor tear which makes twisting difficult - but I'm determined to be back strong next season and won't give up."
Britain's Gary Hunt missed out on the chance to defend his world 27m high diving title - finishing fifth in Budapest, Hungary.