Sam Smith had the only other 007 chart success, when Writing’s On The Wall from Spectre went top in 2015.
Eilish, who turned 18 in December, is the youngest artist ever to record a track for the Bond franchise.
The star performed No Time to Die live for the first time this week, at the Brit Awards in London.
She also picked up the prize for best international female at the ceremony.
No Time To Die racked up 90,000 equivalent chart sales in its first week; including 10.6 million streams.
That makes it the biggest track of the year so far and also the Bond song with the biggest opening week sales.
Smith’s theme shifted 70,000 copies in its first week, while Adele’s Skyfall sold 84,000.
However, Adele’s track was released on a Wednesday, meaning it was only on sale for two days before the chart figures were compiled. In it’s second “week” on the charts, it sold 92,400 copies.
‘Insane writer’s block’
Speaking to BBC Breakfast this week, Eilish said that her brother and musical partner Finneas O’Connell had suffered an “intense amount of writer’s block” as soon as they were given the nod to produce the track.
Having made an unsuccessful attempt at writing it in a traditional recording studio, they eventually came up with the goods while on the road.
“We wrote and recorded the Bond song on a tour bus in Texas,” explained O’Connell.
A meeting with the Bond film boss Barbara Broccoli in Ireland, following one of their live shows, helped the writing process as she gave then “a little hint of the first scene”.
Broccoli followed that up by sending the pair the script for the opening sequence.
“It was so cool to read that,” said Eilish. “It was really helpful, it really wrote the song for us, I think”.