Robert Snodgrass fired a 57th-minute victor for Hull but Claudio Ranieri's Leicester lacked the intensity that underpinned their previous campaign.
Snodgrass's second-half strike sealed the points for City after Riyad Mahrez's controversial penalty had cancelled out Adama Diomande's opening goal.
Although Leicester has managed to keep all but one of its key players from last season with combative midfielder N'Golo Kante moving to Chelsea Claudio Ranieri's team lacked its usual bite and finishing. At the moment, the remit is the same - to take the team and prepare as best we can.
Hull is still without a manager after Steve Bruce left in July, and a club that only secured promotion through the Championship playoffs has been badly hit by both injuries and protests by fans against its owners.
"We tried to win but sometimes it's not possible", Ranieri added. "It was fingers crossed to make sure we had enough players, but full credit to them".
"We started the day saying: 'This is going to be a hard season for Hull and today they play the champions, ' and at the end of the day we are now asking Leicester questions. But he was not at his best today".
Having won the Premiership as 5000-1 outsiders, Leicester City began the new season by doing something no reigning champions have. The Foxes are likely to miss out on the top four this season after what has been an incredible campaign in the last while Hull are favourites to get the drop. The talented, experienced manager's No. 1 goal this season is Champions League qualification, but with their summer signings of Zlatan Ibrahimovic and Paul Pogba, winning the league is realistic.
Ross Barkley had earlier given new manager Ronald Koeman an ideal start to life at Goodison Park with a fifth-minute free kick.
"There were one or two players who I felt were not at it today, Mahrez was a player that frustrated me", Redknapp said. It will not be a surprise if we find another Jamie Vardy next time in May.
Swansea eventually broke through the Burnley resistance to come away with a 1-0 win.
This proved to be a problem when the talismanic Jermaine Defoe slotted underneath Willy Caballero to peg them back in the second half.
Crystal Palace lost 1-0 to West Brom as Salomon Rondon struck the only goal of the game.
Middlesbrough were denied victory in their first top-flight game since 2009 as a 67th-minute free-kick by Xherdan Shaqiri earned Stoke a 1-1 draw after Alvaro Negredo's 11th minute opener.