But a miss in the last jump meant that Nilsson Garip had to settle for eighth place in the end.
The 20-year-old Swede was fourth both after the third and fourth rounds.
Sweden has not won a WC medal in diving in 48 years when Ulrika Knape took bronze in high jump in Cali in 1975.
Emilia Nilsson Garip took EC silver in the three-meter event just a few weeks ago and her strong performance in Fukuoka could mean a place in the Olympics in Paris next summer.
Chen Yiwen, China, won the gold.