The result saw the title holders reach the quarterfinal 8-2 on aggregate.
Kvaratskhelia struck on the night and was also named man-of-the-match. He said afterwards: "I feel great.
"I'm really happy we won against Chelsea – it was not easy as they have quite a good team. It was a difficult game but today was our night. We played our game and it was important we all gave our best. We are happy about that.
"It was important that we scored the first goal quite fast. After that, we just played our game. It would have been difficult if we had conceded, because maybe our game would have changed.
"In every game, we try to back our confidence. We did a great job... we need to continue like that, because there are lot of games ahead."
