The 40-year-old singer made an unannounced entry at the event to play a rendition of the Roy Orbison classic, which was featured on the soundtrack of her 1990 film of the same name.
Roberts, 49, who is a friend of the "Magic" rocker, was being honoured with the Award of Courage in recognition of her support of the fight against AIDS.
Besides other songs, Martin also sang a duet on Sinead O'Connor classic, "Nothing Compares 2 U" along with host James Corden.
To this Corden replied, "Yes, certainly the notion of the chorus is how everybody feels."
Roberts reunited with her co-star Tom Hanks at the event, who presented the award to her.
With the honour, the Oscar-winning actor joins previous amfAR honorees including Charlize Theron, Ryan Murphy, Scarlett Johansson, Jeffrey Katzenberg, Goldie Hawn, Jennifer Lopez, Miley Cyrus, among others.
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