Madonna first took to the stage on Friday while Sabrina was singing Juno, appearing during the lyric "Have you ever tried this one?"
The song then cut to Madonna's Vogue, which the pair sang together, along with Like A Prayer and a new track, which is believed to be from Madonna's upcoming Confessions II.
After the performance, Madonna thanked Sabrina for the collaboration, saying: "Sabrina, thank you so much for inviting me on your show," and Carpenter replied: "No thanks needed, Madonna. You can have whatever you want."
Madonna went on to reminisce about her last performance at Coachella, two decades ago.
She said: "I have a few things I wanna get off my chest. Twenty years ago today, I performed at Coachella. I was in the dance tent, and it was the first time I performed, Confessions on the Dance Floor Part One in America. And that was such a thrill for me, so you can imagine what a thrill it is for me to be back 20 years later in the same boots, the same corset, the jacket I had on earlier, the same Gucci jacket. So, it's like a full circle moment, very meaningful for me.
"So in all circumstances for the rest of the month, let's try to get along, okay? And to that point, the great thing about music is that it brings people together, am I right? It's the one place that people have to put their differences aside, put their shit down, and just everybody have a good time together, right?
 "So I am thrilled to be a part of that healing experience, bringing people together."
Madonna also joked that she was thrilled to perform with Carpenter because she is one of the few pop stars who is shorter than Madonna.
She quipped: "The other thrilling thing I need to point out to everybody right now is this probably the first time I've ever performed with someone who's shorter than me. So, thank you for giving me that experience."
Carpenter replied, "Amen!"
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