Juan Mata gave the Red Devils the lead in the 40th minute when he pounced on an under-hit backpass from Simon Francis which then deflected off Artur Boruc, back into the defender, with the deflection falling kindly for the Spanish midfielder to slot home.
Up until that point, the Cherries had been good value at the Vitality Stadium with manager Howe suggesting the nature of the goal really killed the confidence of his players.
"The game was on a knife-edge until the first goal," said Howe.
"The way the goal's come about was a hard one to take, because it looked as though we'd got away with the mistake, and then for the unlucky ricochet we concede.
"And that moment's tough, when you give a team like Manchester United the lead."
Right-back Adam Smith produced a top quality finish with his left foot on 69 minutes to pull one back for Bournemouth but the damage had already been done on the south coast.