In a repeat of last year's Olympic final in Rio de Janeiro, the destination of the gold came down to a straight fight between the ever-consistent 27-year-old Stefanidi and American Sandi Morris.
In Rio, Stefanidi had won on countback but this time the victory was much more emphatic as she had 16 centimetres to spare over Morris, clearing a national record 4.91 metres to her rival's 4.75m.
It meant that Stefanidi, who has been winning championships since she took the world youth title 12 years ago and has been unbeaten in eight competitions this summer, added the world crown to her Olympic and European titles.
She wrapped up her latest victory with a first-time clearance at 4.82m, having brushed the bar faintly, as Morris, having failed once at that height, then gambled on pushing the bar up to 4.89m and failed twice.
Freed to enjoy herself, Stefanidi had the bar raised to 4.91m which she cleared, again brushing the bar, to add five centimetres to her national record and record the best leap in the world this year.
Then, she tried to break Yelena Isinbayeva's championship record but had three failures at 5.02m. Still, it did not stop her having fun, parading with the national flag as the strains of Zorba the Greek rang round the stadium.
Cuba's defending champion Yarisley Silva and Venezuela's Robeilys Peinado were both awarded bronze medals. The pair could not be separated on countback, having both cleared 4.65m. Peinado's vault equalled her national record.
(Reporting by Ian Chadband, editing by Neil Robinson)
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