Leaked images appear to show the couple recreating Patrick Swayze and Jennifer Grey's romantic clinch from the 1987 rom-com at a bash celebrating One Direction's Madison Square Garden concert last week.
"It was brilliant. The song came on and they just started dancing together," a source told The Sun.
"They didn't know it from start to finish, but towards the end they had a little chat, then she took a run and jumped into his arms. Everyone was laughing and egging them on."
Also at the after-party was Ed Sheeran, who joined One Direction on stage to perform their single 'Little Things', and Little Mix's Perrie Edwards, girlfriend of band member Zayn Malik.
The release of the pictures comes after footage of Styles and Swift kissing at the Z100 Jingle Ball in New York was leaked online.
The pair are alleged to be staying at a romantic cottage on the outskirts of Manchester after Swift accompanied Styles to the Capital FM Jingle Bell Ball and the X Factor final last weekend.