But the interruption did not help the singer, representing the UK, win points with viewers as she finished 24th out of 26 at the annual contest.
Israel won the competition which this year was held in Lisbon, Portugal, and watched by an estimated 200m people.
SuRie chose not to perform again after an intruder snatched her microphone in the middle of her performance of her song Storm and shouted about "Nazis of the UK media," adding: "We demand freedom."
After the event, the 29-year-old tweeted: "Well, I've always said anything can happen at Eurovision ..."
She said: "I'm so proud of my performance tonight. I gave it my very best.
"It's been an incredible experience for me. I am so grateful for everyone's love and support. The fans make Eurovision what it is; the biggest and the most inclusive and open celebration of music in the world.
"Eurovision is a family, and I am proud to be part of it."
A man, dressed in a black and red bandana and slogan t-shirt promoting a book available on Amazon, was taken into police custody shortly after he was rushed off the stage by security guards after interrupting the performance.
A man dressed in the same bandana and t-shirt stormed the stage of the National Television Awards, where he was ordered off by host Dermot O'Leary.
Northern Irish talk show host Stephen Nolan also claimed the same stage invader crashed his programme last year.
A statement from European Broadcasting Union, which operates Eurovision, said: "The EBU regrets a stage invasion took place during the United Kingdom's performance at the Eurovision Song Contest Grand Final in Lisbon this evening.
"The person responsible is currently in police custody.
"The UK singer SuRie and her team were offered the option to sing again but decided not to because they were extremely proud of her performance and have decided that there is absolutely no reason to perform the song again."
The incident left SuRie without a microphone for at least ten seconds and she was forced to clap along as cameras cut to fans in the audience.
She later resumed her song and finished to rapturous applause.
After the performance, Graham Norton who is serving as commentator for the BBC's coverage said: "She was doing a brilliant job anyway.
He later added: "We don't know why he stormed the stage but it doesn't matter, you don't hijack someone's hard-earned moment in the spotlight, no matter what your cause."
Israeli entry Netta won the contest with her song TOY, which featured an unusual chicken dance.
As she collected her trophy, she said: "I'm so happy. Thank you so much for choosing different, thank you for accepting difference between us.
"Thank you for celebrating diversity. I love my country. Next time in Jerusalem!"
Stars rushed to offer support to SuRie after the stage invasion, with The Fizz's Cheryl Baker tweeting "love your heart".
She added: "I wonder if they'll ask @surieofficial to perform again? She must be in a state of shock. Where was the security? He could have had a weapon!"
Author JK Rowling wrote: "That was everyone who's ever been on stage's worst nightmare and it must have been scary, but what a pro, what a recovery @surieofficial."
Presenter Scarlett Moffatt tweeted: "Hope surie is ok. She is an absolute star."
Former Home Secretary Yvette Cooper added: "That was actually excellent #SuRie #eurovision - pumped it up even better for being interrupted."
The Eurovision stage was invaded last year by a man draped in an Australian flag, who flashed his bare bottom at the audience.