Burnley, who have claimed just seven points away from home all season, equalised against the run of play through Sam Vokes' 83rd-minute header but, with a draw beckoning, King netted his 16th league goal of the season two minutes later to seal a deserved win.
Bournemouth -- whose previous highest top-flight finish was 16th a year ago -- sit 10th with 45 points from 37 games. Burnley, meanwhile, are five points behind them in 14th.
(Reporting By Tom Hayward,; Editing by Neville Dalton)
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