Wanderers twice lead in the Midlands, first through Clough in the opening stages and again in the second half following an own goal from Kieran Fenton.
However Forest responded to both of Bolton’s goals to take the game to extra time with Samuels striking the winning goal in the 101st minute to book the Reds’ place in the last four.
It was consequently the end to a fantastic run in the FA Youth Cup for Bolton’s youngsters and they can walk away with their heads held high after a spirited performance.
David Lee and Tony Kelly named an unchanged starting line-up against Forest after their 12 goal thriller against Spurs at White Hart Lane.
Number seven Craig Lester, who was on the bench for the first team against Sunderland in January started on the right wing whilst Niall Maher captained the side.
Like their first team counterparts have done in their last two games, Wanderers U18’s started at full speed and hit Forest with a deadly blow with only two minutes played by taking the lead.
A cross field pass to the left wing was collected by number nine Clough, taking the ball under control the striker cut inside Reds full back Michael Hollingsworth and unleashed an unstoppable right footed effort from 25-yards into the top corner.
Lee and Kelly’s side came close to a second on the quarter hour mark, midfielder Dillon Wolstenholme cutting open the Red’s defence with a through ball into the path of Lester.
Racing clean through, Lester had only the goalkeeper to beat, however custodian Jordan Smith was quick out from his line and did enough to distract the winger with Lester hitting wide.
In the 18th minute Forest levelled matters at the City Ground. Scottish midfielder Jack Blake powered his way past the Wanderers back line and squared the ball to team mate Ottim inside the penalty area for a simple finish from five yards out.
Forest’s equaliser lifted their spirits and they went in search for a quick fire second only to prevented by Jan-Ole Sievers’ cross bar.
Still in advanced position from a corner kick, centre half Lawrence Gorman received the ball on the edge of the penalty box after a tame clearance and unleashed a powerful effort only to rebound back off the frame.
However on the half hour mark it was the Whites’ turn to hit the woodwork in an open FA Youth Cup quarter final with both teams vying to face either Everton or Norwich City in the last four.
Referee Stephen Martin played a good advantage and allowed play to continue after Tom Youngs was fouled just inside his own half.
Lester continued and flew past the Forest full back but from an acute angle could only hit the post with the score remaining 1-1.
For the remainder of the first half, Forest sustained pressure with Blake a constant menace and dictated play in the heart of midfield.
The teenager created the final chance of the half hitting a 20-yard strike inches wide. The half time whistle went with everything still to play for in the second half.
It was a quiet start to the second period for both sides in terms of chances with neither goalkeeper tested.
Management duo Lee and Kelly will have been pleased with the way their side were defending as they continued to block any attack thrown their way by the hosts.
In the 65th minute, Bolton made their first change, Kieran Nolan introduced for Sam Bailey with the prospect of extra time and penalties on the horizon.
But five minutes later Bolton regained the lead and put one foot into the semi-finals when Forest centre half Kieran Fenton put the ball beyond his own goalkeeper.
A 40-yard switch from left to right picked out the run of Lester, showing a magnificent first touch the winger diverted a low cross into the penalty area and under pressure from Youngs, Fenton slid the ball into his own net.
With quarter of an hour to go, Forest made their second change of the evening, Jordan Palmer Samuels coming on in place of Wilfred Gnahore.
It turned out to be an inspired change from the Nottingham Forest bench and Samuels’ first contribution was to level proceedings inside forty seconds of coming on.
The youngster, operating on the right flank, weaved his way through the Bolton defence and rifled into the far corner to the jubilation of the home support.
Forest had two glorious opportunities to win the game in the dying stages with both Otim and Morgan Ferrier trying the luck from distance but unable to find their way past Sievers. The full time whistle blew with the tie going into extra time to decide the winner.
In the early stages of the first period, it was clear to see both teams were wary of pushing to many players forward in case any mistake were made.
With 101 minutes played, Nottingham Forest took the lead when sub Palmer-Samuels hit his second of the evening and handed the Reds the lead for the first time.
The winger had team mate and fellow sub Danny Elliott to thank for the goal, with Forest’s number 15 supplying Samuels from the left wing with a perfect delivery for a simple tap in.
The first period of extra time came to an end with Forest now in the driving the seat. Ahead of the second period Bolton made their next change as they went in search of an equaliser, Thomas Walker replaced by Elliott Newby.
Bolton made their final change with Harry Campbell coming on in place of Jordan Hendrie but despite their valiant efforts Wanderers couldn’t find a way back into the tie with the score finishing 3-2 to the hosts with Forest advancing to the semi-finals.
Wanderers: Sievers, Hendrie (Hamer,112) Gibson, Holding, Maher, Bailey (Nolan, 65) Lester, Wolstenholme, Clough, Youngs, Walker(Newby, 105). Unused subs: Abbotts, Campbell.
Forest: Smith, Hollingsworth, Kamaneno, Blake, Gorman, Fenton, Gnahore (Palmer-Samuels, 75), Wallace, Otim, Ferrier, Thomas (Elliott, 55). Unused subs: Ackroyd, Polimos, Myles.