At 2-2, Chiesa scored in the 88th minute to put Liverpool 3-2 ahead before Mohamed Salah rounded off the scoreline at 4-2 in injury-time.
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Afterwards, Chiesa said: "I enjoy Liverpool very much. I will talk to the club, but I want to stay here and fight to win many titles."
The Italy attacker dedicated the goal to the memory of former teammate Diogo Jota and his brother Andre Silva.
He added, "It was a great moment for me... but my thoughts go out to Diogo. It was very emotional for me.
"After the goal, I must say that my thoughts went to his family, to his brother André. That's all I can say."