Bournemouth took the lead through Antoine Semenyo, who finished confidently to put the hosts ahead.
United's struggles continued as they laboured against a spirited side, even after the home team were reduced to ten men when Evanilson was sent off with 20 minutes remaining.
Despite their numerical advantage, United found it difficult to break through.
Ruben Amorim's men were relentless, registering 25 shots during the match, and it took until the 96th minute for United to find a way through. Manuel Ugarte's driven effort was diverted into the net by Hojlund, rescuing a point for the visitors.
The goal was only Hojlund's fourth in 29 Premier League appearances this season, reflecting Manchester United's broader struggles under pressure.
Across all competitions, the Danish striker now has nine goals and four assists from 46 appearances - a return that highlights the difficulties United have faced in attack.
"We could do better," Amorim told Sky Sports. "We created chances but we need to do better near the box. It is the small things. We have to understand the foot that is in play, crossing, one v ones. We need to understand the game in that way."
Asked about Hojlund, he added: "It is always important for strikers to score. But when we look at the game as a striker it is not just the goals. It is a good boost but the next game is a new history and we have to go again."
Ruben Amorim has stated that he holds "no regrets" regarding his decision to take the managerial position at Manchester United, but acknowledged that the timing of his appointment may not have been ideal.
Ian Wright has ignited a transfer frenzy by tipping Marcus Rashford to thrive at Newcastle United, claiming the Manchester United loanee would be "dangerous" for the Magpies.
Liverpool are fighting tooth and nail to keep their star right-back Trent Alexander-Arnold, with reports emerging that they have tabled a blockbuster contract offer to fend off interest from Real Madrid.
Manchester United have set their sights on Atletico Madrid's Jan Oblak as a potential replacement for Andre Onana, with the Spanish giants reportedly ready to part ways with their long-time goalkeeper.
