Sunderland have been relegated from the Premier League after losing 1-0 at home to Bournemouth as Hull drew 0-0 at Southampton.
David Moyes' side headed into their game knowing their fate would be sealed if they failed to match the Tigers' result at St Mary's.
Both games were goalless heading into the final few minutes, but in the 88th minute Josh King netted the winner for the Cherries at the Stadium of Light.
The Black Cats nearly had a reprieve when Southampton were awarded a penalty for Alfred N'Diaye's foul on Maya Yoshida, but Dusan Tadic's stoppage-time spot-kick was saved by Eldin Jakupovic.
The results left Sunderland 13 points behind fourth-bottom Hull with four games left.