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.
Forest keeper Dean Henderson produced a superb save to palm away a Trent Alexander-Arnold header in the final 10 minutes.
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.
