The moment was caught on camera and shows the pair taking it in turns to sing parts of the 1997 hit, before joining in together for the chorus.
Rodrigo had previously given a surprise performance of the track at Bunny Jackson’s bar in Manchester after her show at the Apollo last week (3 July).
With a host of a-listers having joined Rodrigo on stage throughout her Sour tour, the 19-year-old is getting a reputation for surprise guests.
Last week at Glastonbury, Rodrigo welcomed Lily Allen to The Other Stage where the pair sang Allen’s song “F*** You” to the US Supreme Court (following the court’s controversial Roe vs Wade ruling).
Across the American leg of the tour, she was joined by Avril Lavigne to sing “Complicated” and Alanis Morissette for a cover of “You Oughta Know”.
“Torn” originally topped the charts after it was covered and released by Imbruglia in 1997.
Despite being associated with the Australian pop star, the rendition was actually the fourth version of the song to be recorded. The track was originally written by LA band Ednaswap.
Rodrigo will take to the Eventim Apollo stage for the second time tonight (7 July) for the final show of her Sour tour.