Pink, Brandi Carlile Honor Sinéad O'Connor with 'Nothing Compares 2 U' Duet

Sinéad O'Connor's death is prompting an outpouring of love from other artists ... like Pink and Brandi Carlile, who paid their respects with an incredibly moving duet of her signature hit.

The 2 singers joined forces Wednesday night in Cincinnati, where they marked Sinéad's passing by performing "Nothing Compares 2 U" for the crowd at Pink's Summer Carnival tour.

It's a pretty emotional live performance -- the track, written by Prince, is about heartbreak and the feeling of being alone after losing someone ... a fitting song in light of Sinéad's death.

As we reported, Sinéad was found dead in a London home Wednesday morning -- Scotland Yard says cops responded to a report of an unresponsive woman, but nothing was able to be done to save her once they arrived.

Sinéad faced tragedy in recent years, including the death of her 17-year-old son, Shane, who died by suicide last year. A cause of death for the 56-year-old singer has yet to be determined.