The 29-year-old had held the previous best of five metres set in Donetsk in February 2009.
Isinbayeva, who also holds the outdoor world record of 5.06m set in Zurich in August 2009, has now set 28 world records in her career.
“I’m so happy to come back at this level, I’ve been dreaming about this,” she told TV4 news after setting the record on her second attempt.
Double Olympic champion Isinbayeva had already clinched first place at 4.92m, ahead of Britain’s fast-improving Holly Bleasdale and Cuba’s Yarisley Silva who both finished at 4.72m.
Isinbayeva’s latest world record comes just over two weeks out from the world indoor championships in Istanbul.
It was also her third win of the year to follow victories indoors at Volgograd, Bydgoszcz and Lievin, although until Thursday, she hadn’t got beyond the five-metre mark.
Bleasdale enjoyed first-time clearances at 4.52m and 4.72m before Isinbayeva, starting at the latter height, entered the event, succeeding on her second attempt.
At 4.82m, Isinbayeva went clear first time but Bleasdale failed three times.
The Russian then cleared 4.92m before succeeding at 5.01m on her second attempt.