In the third round of the FA Cup, the Championship strugglers defeated the English clubs.
The first goal was scored by Marvin Ekpiteta in the 17th minute.
Forest had a number of chances to draw level at the road.
Ian Poveda and Jerry Yates both scored in the second half.
The fourth-round draw will be held on Sunday.
Forest's exciting run to the quarter-finals last season helped them push for a return to the top flight.
Steve Cooper's team selection suggested that Forest were focused on avoiding an immediate return to the Championship.
James Husband volleyed narrowly wide of the far post before Forest failed to deal with Hamilton's left wing cross and Shayne Lavery's shot found Ekpiteta. The centre-half stabbed the ball into the net after staying forward following a free-kick.
Ekpiteta made two important blocks in the second half as Forest were on top.
Neco Williams gave the ball to Yates, who ran into the box to score.
Hamilton exchanged passes with another sub, Kenny Dougall, before hitting a fine volley inside the far post from the left side of the box, and Yates wrapped up a fine win with a half-volley.
Cooper gave several of the players who have not played a lot a chance to impress. They didn't accept it.
In the first half, Williams and Dennis both went close to scoring.
Lewis O'Brien was off target in the second half.
Yates came off the bench and headed in from Toffolo's cross in the final minute of the game.
Cooper said there could be more signings in the January transfer window as Forest try to stay out of the bottom half of the table.
They have a chance to reach a first cup semi-final in 22 years if they beat Wolves in the Carabao Cup.
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