United have lost just once in their last 10 games but Ruben Amorim will be frustrated as more points at home were frittered away despite arguably the best attacking display of his reign in charge.
Amad Diallo and Casemiro gave the hosts a half-time lead either side of Antoine Semenyo’s equaliser.
Two Bournemouth goals from Evanilson and Marcus Tavernier in seven minutes at the start of the second period turned the game around.
The Red Devils roared back through a brilliant Bruno Fernandes free-kick and Matheus Cunha’s second goal for the club.
However, after failing to beat 10-man Everton and struggling West Ham at home in recent weeks, United let another two points slip away.
Eli Junior Kroupi’s fine finish secured a point for Bournemouth, who should have even snatched victory in stoppage time as David Brooks was twice denied by Senne Lammens.
The Cherries’ winless run stretches to seven games but a point edges them up to 13th.
United move ahead of Liverpool on goal difference into sixth.
Not since May 1984 have United lost a home league game that they were leading at half-time. (AFP)