August 25, 2015 11:13 AM EDT

We were all under the impression that Taylor Swift had exhausted the world’s finite supply of celebrities willing to prance merrily onstage with her during her 1989 tour. Turns out we were horribly mistaken: Last night at LA’s Staples Center, Swift extended a (metaphorical) middle finger to her #haters by bringing out the Queen of Angsty Breakup Songs herself, Alanis Morissette.

As Morissette took the stage, Swift credited the indie chanteuse as a major source of inspiration. “She defined the music of her decade. She inspired a generation of confessional female singer-songwriters who all of a sudden felt like you could actually say these raw feelings that you had; you could actually sing about your real life, you could put detail to it.” Apparently, we can thank Jagged Little Pill for indirectly giving us Red—reportedly about Swift’s painful breakup from Jake Gyllenhaal—and Welcome To New York, about Swift’s painful breakup from wherever she was living before New York.

Swift added, “And I think it’s fair to say that so many of the female singer-songwriters of my generation, including myself, would not write the way that we do without her and her music. And she has written some of the most brilliant music—in particular probably inarguably the greatest breakup song of all-time.”

Swift was referring, of course, to “You Oughta Know,” Morissette’s scathing screed allegedly directed at Full House’s Dave Coulier, a pop-culture factoid that never becomes less baffling. The two then joined forces for what is likely the first and last rendition of the song ever performed by someone in a head-to-toe leather bodysuit.

Here’s a clip from the performance, including what looks like a last-minute attempt by Taylor to hug Alanis, who casually rebuffs her. It’s not fair to deny her, Alanis. But we wish nothing but the best for you both.

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