Huddersfield equalled the record for the earliest relegation in a Premier League season as second-half goals from Luka Milivojevic and Patrick van Aanholt earned Crystal Palace all three points at Selhurst Park.
The Terriers’ defeat, combined with victories for Burnley and Southampton, confirmed the visitors’ demotion back to the Championship.
Milivojevic sent Ben Hamer the wrong way from the penalty spot in the second half after Wilfried Zaha had been fouled by Juninho Bacuna.
Patrick van Aanholt’s composed finish secured a valuable victory for Palace, who move eight points clear of the bottom three.
Jan Siewert’s side spurned several chances to open the scoring in the first half, with Chris Lowe twice forcing fine saves from Palace goalkeeper Vicente Guaita.
Karlan Grant also missed an excellent opportunity with the score at 0-0, firing wide of the target with only Guaita to beat.
Huddersfield become the first Premier League team since Derby in 2007-2008 to be relegated in March.