Isinbayeva, who accumulates world records at the same rate as former men's champion Sergei Bubka, defied difficult, windy conditions to win with 4.91 metres, surpassing her own mark by one centimetre.
Former gymnast Feofanova, the world champion, was second with 4.75 and Anna Rogowska of Poland took the bronze with 4.70.
It was Isinbayeva's seventh world record this year yet the 22-year-old had been close to tears moments earlier, holding her head in her hands.
Her dramatic victory came from an inspired gamble.
In the bronze position and one jump away from defeat after failing at 4.70 and 4.75, and with Feofanova and Rogowska ahead of her, Isinbayeva put up the bar to 4.80 and cleared majestically, earning one of the biggest roars of the night from a sell-out Olympic stadium.
She then emphasised her domination by clearing 4.85, then sailed over the record height as tears welled up in her eyes again. Her feat -- the first athletics world record in Athens -- so impressed Feofanova that the pair, who have publicly admitted that they do not get on, exchanged friendly words and smiles after the event. The pole vault always looked like a two-horse race, the Russian pair having exchanged the world record almost month-by-month over the past two-and-a-half years.
They share nothing else in common.
Isinbayeva is dark-haired, tanned, wears make-up and plays to the crowd. Feofanova is red-haired, freckled, frowning and as pale as a ghost. They also live in different cities, with Isinbayeva describing theirs as a "hi and goodbye" relationship.
The pair both came in at 4.40 and cleared without scares up to 4.65, Feofanova looking the more tense while Isinbayeva, soaring over each time, won over the crowd with blown kisses.
After around two-and-a-half hours of competition, interrupted by track finals and medals ceremonies, the medallists were decided, with only the colours to sort out.
But Isinbayeva inexplicably dislodged the bar on the way down at 4.70 and failed again at 4.75.
Close to tears, she covered herself with a towel to compose herself before her triumphant finale.
There had been tears in the qualifiers as well, when 2000 Olympic champion Stacy Dragila failed to reach the final. The American blamed new shoes for her inept performance.
