The 32-year-old star recently supported her friend Taylor Swift at one of her concerts at London's Wembley Stadium earlier this month but disaster almost struck when her team forgot to collect the designer gown before the show and the building was locked up.
Suki recalled to The Times newspaper: "So one of my managers gave a porter £500 to break in and grab the dress. I think there were literally 140 [phone] calls."
The dress eventually arrived at the venue at 3.30pm, less than two hours before Suki was due on stage but the 'Daisy Jones and the Six' star hadn't been told what happened beforehand.
She explained: "Because I was already stressing".
Suki had personally called the brand's creative director, Chemena Kamali, to make the dress.
She admitted: "I've never asked anyone to make me a dress before. I always get really scared they'll say no. But I called her, and she was like: 'Yes, I'd love to.'...
"I always want massive sleeves. I want to be able to throw my arms up in the air."
The idea of supporting the 'Karma' hitmaker was first suggested by the 34-year-old pop star to her friend over a year ago, but it wasn't until Suki performed at Coachella in April that the booking was confirmed.
She recalled: "Taylor did mention [the idea of] that at dinner a year ago. I didn't know if it was real. But that's the thing about her: I should have known, she always plans. When she says something, she's gonna do it...
"My dad kept saying: 'Guess it's not happening then ... shame about that.' I was like: 'No, Dad, I promise, you are coming to Wembley!'"
Suki - who has a five-month-old daughter with partner Robert Pattinson - first met Taylor "during a really fun summer in New York almost 10 years ago".
She added: "I was there shooting a movie. It was one of the great summers.
"A bunch of people were in town, all these girls were hanging out. I remember being on her rooftop and having a really great time. And I have some memory of me, like, talking to — oh, I probably shouldn't say!"