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 earn 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' men's dominance became more prominent.
Marcus Tudgay's header was followed up by a wonderful David McGoldrick strike in the second half as Forest gave themselves an opportunity to reach the promised land after a 12-year absence.