United twice went close to opening the scoring in a bright start in wet and windy conditions. Andreas Pereira fired over while Daniel James' long-range effort went narrowly wide.
AFC Bournemouth fought back and took the lead on the stroke of half-time. Adam Smith crossed for King, who, against his former side, flicked over Aaron Wan-Bissaka and volleyed beyond David De Gea.
The home side had more opportunities to double their advantage after the break as Callum Wilson forced De Gea into a fine save on 75 minutes.
A first victory in five matches moves AFC Bournemouth up to sixth on 16 points, above Man Utd in eighth with 13 points.
AFC Bournemouth: 9 Nov v Newcastle (A)
Man Utd: 10 Nov v Brighton (H)