The point moved United up to 14th in the standings.
Semenyo fired a low shot from inside the box to beat United goalkeeper Andre Onana in the 23rd minute.
Bournemouth had chances to extend its lead with Dango Ouattara hitting the post with a free kick after the break. But when Evanilson was sent off for a lunge on Noussair Mazraoui following a VAR review in the 70th, United began to increase the pressure.
The visitors still had to wait until the sixth minute of added time for Hojlund to divert Manuel Ugarte's effort past Kepa Arrizabalaga.
Liverpool needs only one point at home to Tottenham later Sunday to clinch the Premier League title.
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James Robson is at https://twitter.com/jamesalanrobson
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AP soccer: https://apnews.com/hub/soccer
Credit: AP
Credit: AP
Credit: AP
Credit: AP
Credit: AP
Credit: AP