The world silver medallist became the first non-Russian to win the title since Ukraine's Olena Vitrichenko in 1997.
It was Israel's second gold medal of the Championships, after they won the group title on Friday.
Ashram actually received the same number of total points – 100.900 – as silver medallist Alina Harnasko of Belarus, but won gold by having a lower total execution technical deduction across the four apparatus.
Harnasko's teammate Anastasiia Salos won bronze.
Bulgaria's Boryana Kaleyn was in contention for a medal before she dropped a club during her routine on her final rotation.
Harnasko and Salos had drawn early start orders in the rotation, allowing the Belarusian pair to lay down a marker.
That meant Ashram knew the exact score she needed on her final routine, the hoop, to clinch victory.
It was a watch-in-awe routine that did not appear to contain the slightest hint of an error, as perfect a routine as the Israeli needed it to be to get the score she required.
While there were no Russians taking part in Kyiv due to the ongoing global health situation, it should not detract from Ashram's victory as she still faced stiff competition from the Belarusians.
Ashram's score of 26.500 on the hoop topped the charts of all athletes, while Harnasko placed first on each of the other three apparatus.
However, with their total scores and execution scores tied, it came down to the second tie-breaker to split the pair.