Sunderland's 10-year stay in the Premier League ended with defeat against Bournemouth at the Stadium of Light.
The result coupled with Hull City's draw at Southampton means David Moyes' side are 13 points from safety with four games left.
Bournemouth's Joshua King scored the only goal with just two minutes left, tapping home from Ryan Fraser's pass.
The Norwegian also came close in the 20th minute but his shot rebounded off the post and crossbar and into the arms of Jordan Pickford.
Artur Boruc saved from Jermain Defoe in the first half, and Fabio Borini and George Honeyman in the second, but the Black Cats failed to sustain any real pressure on the Bournemouth goal.
They have now been relegated from the Premier League for a joint-record fourth time.
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