The Tigers had not beaten United in league action since 1974, but they produced a fearless performance to spoil Michael Carrick's first Premier League opener as United manager.
Hull made the stronger start and quickly tested Senne Lammens. The United goalkeeper denied Bryan Mbeumo and Matheus Cunha before saving from Oli McBurnie's powerful header.
Ryan Giles then saw his effort tipped over, while Lammens was forced into another excellent save from the resulting corner when McBurnie's header was pushed onto the post.
Hull finally broke through when Semi Ajayi reacted quickest to finish from the corner and send the home supporters into wild celebrations.
United struggled to respond. Patrick Dorgu was presented with two chances by Bruno Fernandes and Harry Maguire but failed to find the target, while Mbeumo's acrobatic effort was deflected behind by debutant Nobel Mendy.
Mendy then made an even bigger impact at the other end. The defender met Regan Slater's superb free-kick delivery and calmly guided his finish past Lammens to give Hull a deserved 2-0 lead.
John Egan then blocked a Fernandes effort as Hull reached half-time with their advantage intact.
Carrick introduced Marcus Rashford at the break in an attempt to change the game, but United continued to struggle against a disciplined Hull defence.
Ayden Heaven headed wide, while Hull remained dangerous on the counter-attack. McBurnie produced an impressive run through the United defence before Mohamed Belloumi fired over from distance.
Hull suffered two injury setbacks as Mendy and Lewie Coyle were forced off within seven minutes of each other, but the Tigers refused to lose their momentum. Substitute Cody Drameh almost added a third late on.
Lammens was eventually called upon to deny Mbeumo again, while Harry Maguire's long-range effort was comfortably saved as United failed to find a way back into the contest.
The victory gave Sergej Jakirovic a memorable start as the first Bosnian manager to take charge of a Premier League match.
