The victory means Billy Davies' side will now tackle Swansea in the play-off semi-finals after Brendan Rodgers' men leapfrogged bitter rivals Cardiff into third place.
Forest will hope to improve on last year's effort in the season finale when they were beaten by Blackpool - who went on to secure a place in the Barclays Premier League - at the last four stage.
Going into the encounter, the visitors knew they needed just a point to secure a place in the end-of-season shake-up while Palace had little to play for given they ensured safety last week.
And the difference between the sides' ambitions showed in a one-sided clash which Forest dominated throughout.
They were set on their way by Lewis McGugan's 17th-minute strike and, after Eagles centre-back Dean Moxey was sent off, Davies' side became more dominant.
Marcus Tudgay and David McGoldrick added goals in the second half as Forest gave themselves an opportunity to reach the promised land after a 12-year absence.
Spurred on by the possibility of a play-off berth, the visitors showed intent from the off and almost took the lead in the ninth minute.
McGugan further underlined his credentials from set-pieces to deliver an excellently directed corner which Luke Chambers headed against the crossbar.
They did not have to wait much longer to open the scoring, though, with McGugan putting them ahead with a typically classy finish.
Anthony Gardner failed to get any distance on his headed clearance from a hopeful long ball, allowing McGugan to fire home a well placed volley from a tight angle.
Any hopes Palace had of claiming anything from the game were hampered significantly in the 25th minute when Moxey received a straight red card for a high challenge on Tudgay.
Davies' men dominated for the rest of the opening period, while Palace's one-man disadvantage was showing as they offered little threat.
Whatever Dougie Freedman said to his players at half-time appeared to work as the hosts showed more endeavour in the second period.
However, they failed to transfer that into clear-cut chances as Forest continued to enjoy a worry-free afternoon.
The visitors continued to create the better opportunities and they all but guaranteed a play-off spot in the 69th minute.
Brendan Moloney was the orchestrator, sending in a delicious right wing cross which Tudgay headed home.
McGoldrick added further gloss to the scoreline with 10 minutes remaining through a moment of real quality, picking up the ball 25 yards from goal before unleashing an unstoppable effort past a helpless Julian Speroni.
Cardiff's 1-1 draw at Burnley, coupled with Swansea's 4-0 victory over relegated Sheffield United, means Forest will take on the Swans in the semi-finals.
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