Arsenal boosted their Champions League hopes with a deserved victory over West Ham, who remain in relegation trouble after a fifth consecutive Premier League defeat.
Tottenham staged a late comeback to overcome Swansea and stay in touch with Chelsea.
Chelsea maintained a seven-point advantage over Tottenham at the top of the Premier League with a hard-fought victory over Manchester City.
Joshua King scored a dramatic late equaliser for Bournemouth as Liverpool dropped two crucial points at Anfield.
Swansea 1-3 Tottenham
Arsenal 3-0 West Ham
Hull City 4-2 Middlesbrough
Southampton 3-1 Crystal Palace
Liverpool 2-2 Bournemouth
Chelsea 2-1 Manchester City