Taiwo Awoniyi, who left Liverpool in 2021 without making a competitive appearance, hit the winner from close range after his initial attempt came back off a post.
Liverpool were a long way from their best – Virgil van Dijk wasted their best chance – and remain without an away league win this season.
It could have been worse for the visitors but Brennan Johnson hit a post in the closing moments with Liverpool keeper Alisson well off his line.
There were jubilant scenes on and off the pitch at the final whistle as Forest enjoyed their best day since returning to the top flight this season after a 23-year absence.