Along with her twin sister Jennifer, Gadirova had been part of the British squad who claimed team silver at the M&S Bank Arena, also securing a place at the 2024 Olympics in Paris.
The Dublin-born 18-year-old followed that with a fine effort on Thursday evening to take another place on the podium behind Brazil's Rebeca Andrade and American Shilese Jones.
Gadirova had qualified in fifth for the final, which is where she sat at the halfway stage following two rotations.
After moving up to fourth heading into the final rotation, with Kinsella then in third place, Gadirova produced a stunning floor routine to score 14.400 and put herself into first.
Jones, though, then went to the top of the standings with a 13.700 on the floor, before Andrade - who had been in front from her opening round on the vault - matched Gadirova's score to claim gold and go one better than her silver from last summer's Tokyo Olympics.
Kinsella narrowly missed out on a medal - just 0.134 points behind her British team-mate - after finishing on the uneven bars, with a small step on dismount seeing her score 14.166.
"I am actually speechless. I don't know what to say," Gadirova told BBC Sport.
"I am just over the moon, so shocked with the score and relieved. I just stuck with the training and believing that I could do it.
"I have done all the hard work and so it is time to perform it the best I can and that is what I did."