The former United youngster struck just before the interval as Eddie Howe's side moved into sixth position in the Premier League table, with the Red Devils dropping to eighth as they lost for the fourth time in the league this season.
United had a big chance inside the first three minutes when Daniel James broke down the left before delivering a low cross into Andreas Pereira, but the Brazil international completely missed the ball as Bournemouth escaped a dangerous moment in the early exchanges.
Bournemouth's first half-chance of the match arrived in the 16th minute through Harry Wilson, but the on-loan Liverpool attacker saw his effort deflected behind before Callum Wilson nudged one wide of the post from the resulting corner.
Fred then had one deflected over the home side's crossbar as both teams threatened to make the breakthrough during an incredibly open period of the match.
James was excellent for United in the early exchanges and had a chance of his own in the 21st minute after collecting a half-cleared free kick, but the Wales international's strike just missed Ramsdale's goal.
The pace of the match dropped considerably in the latter stages of the first half, with both teams struggling to find that final pass with the conditions creating plenty of mistakes.
Bournemouth did take the lead on the stroke of the interval, though, with King managing to collect a cross from Adam Smith before lifting the ball over Aaron Wan-Bissaka and finishing from close range.
It was smart work from the former United youngster, but there is no question that Ole Gunnar Solskjaer will have been disappointed with his team's defending as King had far too much time and space, with Wan-Bissaka and Victor Lindelof having to accept a share of the blame.
The first half-chance of the second period also came for Bournemouth, but De Gea did not have to overexert himself to keep out a volley from Fraser after a bright move.
The pitch continued to open up for Howe's side as the half progressed, with King, Callum Wilson and Harry Wilson all finding plenty of space in the final third as United looked more and more nervy at the back.
Ramsdale had to keep out a strike from Pereira just before the hour as United quickened the pace, but Bournemouth were still causing problems down the other end, and De Gea had to save from King and Harry Wilson in quick succession in the 63rd minute.
Jefferson Lerma then struck wide of the away side's goal in the 70th minute just after United had enjoyed a decent spell of possession inside Bournemouth's half of the field.
The Cherries had a super chance to double their lead 15 minutes from time when Harry Wilson found space in a dangerous position, but the on-loan Liverpool attacker could not find a route past De Gea.
Ramsdale then had to keep out a strike from Scott McTominay during a spell of intense pressure from the 20-time English champions.
United continued to force the issue late on but it was not to be for the struggling giants, who have now won just three of their 11 Premier League matches this season, suffering four defeats in the process.
Solskjaer's side are next in action at home to Partizan in the Europa League on Thursday night before hosting Brighton & Hove Albion in the Premier League next Sunday. Bournemouth, meanwhile, will resume their league campaign away to Newcastle United next Saturday.
BOURNEMOUTH (4-4-2): Ramsdale; Smith, S Cook, Ake, Rico; H Wilson (L Cook 86'), Lerma, Billing, Fraser; C Wilson, King
MANCHESTER UNITED (4-2-3-1): De Gea; Wan-Bissaka (Williams 81'), Lindelof, Maguire, Young; McTominay, Fred; James (Greenwood 80'), Andreas (Lingard 68'), Rashford; Martial