Brook, who has been frustrated by injury recently, was in his first fight since October as he looks to get back into the world title mix.
The undefeated Briton has twice had world title fight with Devon Alexander called off, but showed no ring-rust against a man who gave him a hard time 12 months ago.
Brook looked unable to miss in the first round, dominating Jones with his fast jab and finding multiple right-hooks with ease.
He had his man down in the second and looked to be heading for a big finish, only for Jones to survive until the bell.
The American grew in confidence after that, and caught Brook with a few shots of his own, but never did enough to win a round.
Brook stepped up the pace again in round seven, punishing Jones's lacklustre defence with some powerful combinations.
Jones touched down with his glove early in the eighth and continued to be pushed back by Brook onto the ropes, until referee Michael Alexander stepped in and ended the fight.