Dressed in a sheer crop top, black trousers and strappy heels, the 30-year-old was joined on stage by rapper Tinie Tempah who features on the track.
Marking her comeback, this was Cheryl's first performance of her catchy new song, which is part of her fourth studio album set for release in November.
Cheryl's reunion with Simon Cowell on Britain's Got Talent came two months after the music mogul confirmed that she would return as a judge on the X Factor in March 2014.
"There's only so much begging one can take," Cheryl joked about Simon asking her to return. "It's not nice to see a grown man cry, so I finally succumbed."
The pair famously fell out when Simon sacked the former Girls Aloud star from the US version of X Factor in 2011, but the new dad has since admitted that he made a mistake and the troubles appeared to have been forgotton when Cheryl took to the stage during Saturday night's final.
"You know what, I've been doing this for a long time. You have fallouts," said Simon. "I held my hands up and said I was sorry, and I was sorry."
On Thursday Cheryl shared a photo on Instagram giving followers a sneak peek behind-the-scenes of her video for Crazy Stupid Love, showing off her impressive stomach muscles as she dances on set.
Cheryl's video for Crazy Stupid Love will premiere on 9 June
"The video isn't what I've done before," she admitted. "In terms of lighting and stuff, it's a bit more grimy. Because the song's quite up, and pop, it's got that feel, so I wanted it to have the urban twist. It's a bit more of that urban vibe."
The new single, which will be released on 20 July, has already received positive feedback from fans, with comparisons being made between the Geordie beauty and pop superstar Beyoncé Knowles.
It's been a busy few weeks for Cheryl, who also attended the 2014 Cannes International Film Festival in May with her new boyfriend Jean Bernard Fernandez Versini. The handsome frenchman is Cheryl's first romance since her split with backing dancer Tre Holloway last year. The couple also made their first British public appearance at London's Chiltern Firehouse in May.