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".
The finished song is a dramatic, unsettling ballad that hints the plot will centre around the secret agent's betrayal, the BBC's Mark Savage noted last week.
The lyrics to No Time To Die reference lies and deceit, as Eilish sings: "You were never on my side."
Daniel Craig's final outing as the world's most famous British secret agent arrives in cinemas in April, and Eilish said the actor had a "big say" in who wrote the film's opening track.
She admitted they'd already seen a "half-done" version of version of the film (minus their track), which looked "amazing".
The star performed the new song alongside an orchestra, Smiths guitarist Johnny Marr and composer Han Zimmer at Tuesday's Brit Awards.
Speaking to the BBC's Colin Paterson backstage, she dedicated the performance to her fans.
"It was really nice that there were fans right up front that I could look at and smile at. I feel like that was the peak of it for me," she said.
"They always prove to me every time I doubt myself that I don't need to, because they are there."
She added: "They really make me feel better about myself and make me feel like everything I do is worth it… I'm human, man!"
Eilish also revealed that her own favourite ever Bond song is... Adele's Skyfall.
"I dunno, Adele is just Adele," she laughed. "You've gotta give it to her."
How have other Bond themes fared in the charts?
While Eilish and Smith both reached the chart summit, two other official songs from the movie franchise have taken the number two spot.
Duran Duran's A View To A Kill peaked at number two in 1985, as did Adele's Skyfall in 2012.
Despite winning an Oscar and a Golden Globe, Adele's effort was denied the top spot by Swedish House Mafia's Don't You Worry Child.
Shirley Bassey's Goldfinger, in 1964, could only reach number 21 and when the Welsh singer returned in 1971 declaring Diamonds Are Forever, she went to number 38.
Sir Paul McCartney and his post-Beatles band Wings faired slightly better two years later with Live and Let Die reaching ninth place.
The worst performing Bond song was Rita Coolidge's All Time High which reached number 75 in the charts in 1983.
Since 1994, when the Official Charts began collecting sales data, Skyfall has been the most popular song from the franchise, selling 1.1m copies to date.
Almost a year on, the indefatigable record is still hanging around in fourth spot in the album charts, where this week Justin Bieber snatched his second number one with Changes.
Renewed interest in Lewis Capaldi following his Brits double win ensured he pushed Bieber all the way, while Tame Impala's new album The Slow Rush - the week's best-selling album on vinyl - went in at number three.
Fewer than 1,200 chart sales separated the top three.
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