The 26-year-old, who was born in Russia but now represents the host nation, scored 58.765 at the National Gymnastics Arena to take his place on the podium.
"I was performing under the Azerbaijani flag. I feel like an Azerbaijani, I've got the Azerbaijani citizenship and I am feeling very well about this. In the future it will be only better," Grishunin told reporters.
"This is the biggest award of my career. I have this feeling, as if I managed to fulfil a very important task. My coach, my family and all the close people were hoping for me, and I didn't let them down."
"I feel satisfied and relieved. I knew that my mum and my wife are watching me from the stands. I am happy that I didn't let anyone down."