With one game left — at home to Manchester United next Sunday — Hull is third from bottom, two points behind Newcastle and three adrift of Sunderland.
Chadli rounded Hull goalkeeper Steve Harper to slot home in the 54th minute and left back Rose added a second with a powerful shot in the 61st.
Tottenham stayed sixth and kept the team in contention for Europa League qualification.
Hull's loss ensured Aston Villa and Leicester will be in the Premier League next season and reduced the fight to avoid relegation to three clubs. Burnley and Queens Park Rangers are already down.
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