Semi Ajayi opened the scoring in the 17th minute, turning in a rebound after Konstantinos Tzolakis had saved Oli McBurnie's header from a Regan Slater corner, before Nobel Mendy doubled the newly promoted side's advantage on his debut just before the break.
Manchester United dominated possession for long spells but could not find a way through an organised Hull City defence, with Bruno Fernandes seeing an effort deflected wide and Harry Maguire firing straight at Tzolakis as the visitors pushed for a way back into the game. Hull held firm to secure a first Premier League win over United in nine years and hand Michael Carrick's side a losing start to the new season.
Speaking to TNT Sports after the match, manager Michael Carrick did not hide his frustration but insisted the result would not derail his side's season.
"We have a bit to improve on, it was never going to be perfect going behind makes it more difficult, against a promoted team at home, we can't give them much and they had opportunities, we're disappointed but it won't knock us," he said.
Asked where United needed to improve, Carrick added: "It's for us to know and to improve during the week and keep getting stronger as a group and we have a lot to learn from it."
On the two goals conceded, the United boss said: "Two goals is frustrating anyway, they decide the game today and there's things to improve on, one game doesn't change the direction of everything. It doesn't change the direction of the football club."
Carrick was also asked about a potential deadline-day move for Brighton midfielder Carlos Baleba, but declined to be drawn on the subject.
"I had all eyes on this today so any other player, until he's ours, it's not for me to comment on," he said.
Fernandes echoed his manager's frustration when he spoke to TNT Sports, pointing to Hull's threat from dead-ball situations as the difference between the two sides.
"We know in the Premier League these types of away grounds are difficult to play against. You need to match their intensity and aggression. The two set pieces ended up costing us the game today," Fernandes said.
Asked about the mood among supporters after a first-day defeat, the United captain added: "We understand the frustration, every season at the start we want to compete and win every game but we need the fans on our side, and to believe in ourselves."
For Hull, the win capped a dream return to the top flight, and goalscorer Ajayi could not hide his delight when he spoke to TNT Sports.
"It was amazing, it capped off a great start that we had had. I was buzzing to get the goal that got us on our way. I didn't really care if any of us scored, there was no VAR check so I was buzzing that we got the goal," Ajayi said.
The defender was quick to play down suggestions that Hull, widely tipped for an immediate return to the Championship this season, had already made a statement of intent.
"We're not focused on outside noise, we back ourselves to do well and hopefully we will have a really positive season," he said.