Fernandez overcame a 2.46-point deficit from the short programme on Friday to triumph with 273.90 points and beat Olympic champion Hanyu by 2.82 after the free skate.
Kazakhstan's Denis Ten took bronze with a score of 267.72.
"I still don't believe it," Fernandez said. "To beat Yuzu, the Olympic champion, one time, is unbelievable. I don't know if it's going to ever happen again."
Fernandez and training partner Hanyu both fell on quadruple jumps in their routines, but the 23-year-old Spaniard successfully landed two others to gain the advantage.
Hanyu, bidding to become the first Japanese skater to win successive world titles, failed to land his quadruple attempt and had to settle for silver.
"We're team mates, in the competition we're still rivals," said Fernandez, who is coached by Canadian Brian Orser. "Yuzu just told me that he was happy for me. He even dropped a couple of tears."
The 18-year-old Tuktamysheva had a big lead after landing a rarely attempted triple axel in a daring short programme and was able to coast to victory with a free skate routine featuring a triple lutz and double toeloop.
Her score of 132.74 gave her a 210.36 total, way clear of Japan's Satoko Myahara in silver with 193.60.
"I can't believe it yet," the Russian, who failed to qualify for her home Sochi Olympics last year, told reporters.
"I was tight, even with my advantage in points from the short programme I couldn't make any major mistakes. With two major mistakes the advantage would have been gone. It would have been a shame to lose."
Myahara produced a season's best mark but the 17-year-old said there was plenty of room for improvement after putting her hand down on the ice after her second lutz.
Russian Elena Radionova was delighted with her bronze after complaining of feeling ill and weak in her free skate of 121.96, for a 191.47 total.
Radionova, who finished runner-up to Tuktamysheva at the Europeans, edged out American Gracie Gold for a medal.
Gold, who finished fourth at the Olympics, had the second best free skate of 188.96 but the damage was done in Thursday's short programme where she botched her opening triple-triple combination.
"It's always hard to skate a long programme after a rough short programme, because if you can't get through a short well, how could you go through a long programme well?" she said.
(Reporting by Patrick Johnston and Michael Hann, editing by Ed Osmond)
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