Lavillenie eclipsed the Ukrainian great's mark of 6.15m at the indoor event to end his long reign at the top of the all-time rankings.
The 27-year-old's previous best was 6.08m.
He wrote on Twitter: "World record! 6.16m on first attempt. It's unbelieveable, I am still in the air..."
Bubka still holds the outdoor world record of 6.14m.