A sixth goal in four games from Taiwo Awoniyi for the visitors was cancelled out with an effort from Will Hughes after the interval.
Forest made three changes from their heroic efforts against Arsenal that secured their survival last week. Ex-Palace goalkeeper Wayne Hennessey, Willy Boly and Brennan Johnson came in.
The hosts, unchanged from their draw at Fulham, had the first chance when Michael Olise brought a decent save from the keeper after a fine solo run in the fourth minute.
Eberechi Eze almost marked his England call-up with a goal in the 17th minute, after an Olise free-kick was squared to him, but his effort went narrowly past a post.
Palace had the bulk of possession and Nottingham Forest were offering little up front, but they soaked up the pressure and took the lead in an amazing 60-second spell.
They were almost undone on the half-hour mark when a shot by Eze was blocked by Jordan Ayew, with Hennessey turning away a Hughes shot on the rebound.
A long ball out of the Forest half shortly afterwards by Morgan Gibbs-White found Awoniyi, who powered into the area. After getting the better of Joachim Andersen, he followed his goal against Arsenal last week with an effort into the bottom corner.
Odsonne Edouard should have done better with an Olise free-kick after 38 minutes when he put his header wide after finding space in the area.
With Harry Toffolo replacing Renan Lodi for the visitors at the interval, Crystal Palace pushed for an early equaliser. A Cheick Doucoure effort in the 52nd minute was drilled over the crossbar, while a free-kick on the edge of the box three minutes later was put over by Eze.
Delight: Forest had already secured Premier League safety
/ Getty ImagesLike the first half, the home side were generally on top, without forcing a significant opportunity in front of goal. However, they made a breakthrough after 65 minutes, albeit with some good fortune. A cross by Olise into the box was flicked on by Hughes past Hennessey – although the ball deflected off the challenging Boly.
The hosts sent on James McArthur from the bench for his final appearance in a Crystal Palace shirt. With the game finely poised in the closing minutes, both teams, to their credit, were looking for a winner. Forest substitute Emmanuel Dennis fired a tame effort at Sam Johnstone after 81 minutes.
A link-up between Olise and substitute Jean-Philippe Mateta required a last-ditch intervention by Joe Worrall, while Eze fired at Hennessey in the final action of the game – and the season.
