Kenyan midfielder Victor Wanyama scored the game's only goal in the third minute at the KC Stadium, brilliantly lobbing Eldin Jakupovic from 40 yards after the Hull goalkeeper scuffed his clearance.
Arsenal climbed into the Champions League places after Alexis Sanchez scored twice in a 3-0 success at home to winless bottom club Burnley.
Defender Calum Chambers crossed for Sanchez to head Arsenal in front in the 70th minute and smashed home his first senior goal two minutes later after Tom Heaton parried a shot by Danny Welbeck.
Sanchez added a third in injury time from a Kieran Gibbs cross.
Arsene Wenger's side, who welcomed Theo Walcott back from a long-term knee injury, moved into fourth place at the expense of West Ham United, who came from two goals down to record a 2-2 draw at Stoke City.
Missing top scorer Diafra Sakho due to a shoulder injury, West Ham fell 2-0 behind through goals from Victor Moses and Mame Biram Diouf either side of half-time.
But Stewart Downing crossed for Enner Valencia to reduce the arrears on the hour and the Ecuador international returned the favour for Downing to drill home an equaliser with 17 minutes to play.
Earlier, Liverpool slumped to their fourth defeat of the season as Spanish substitute Ayoze Perez earned in-form Newcastle United a 1-0 victory at St James' Park.
Liverpool, for whom striker Mario Balotelli endured another frustrating afternoon, were beaten when Alberto Moreno failed to clear and Perez pounced to lash home in the 73rd minute.
It was Newcastle's fourth consecutive victory in all competitions, following their shock League Cup win over holders Manchester City in mid-week, and saw Alan Pardew's side climb to 11th place in the table.
Runners-up to City last season, Liverpool are now 12 points behind leaders Chelsea, who visit Anfield next weekend.
"We were punished for a mistake and that is what cost us the game," Liverpool manager Brendan Rodgers, whose side visit Real Madrid in the Champions League on Wednesday, told BT Sport.
Balotelli ambled onto the pitch just as the second half kicked off, but Rodgers said "it had no bearing at all on the result", adding: "It is not about Mario Balotelli, it is about the team."
An Esteban Cambiasso own goal saw West Bromwich Albion win 1-0 at Leicester City, while Swansea City midfielder Jonjo Shelvey was sent off for two bookable offences as his side drew 0-0 at Everton.
The weekend's headline fixture arrives tomorrow, when third-placed Manchester City, nine points behind Chelsea, and seeking a first win in four games, welcome derby rivals Manchester United to the Etihad Stadium.
- AAP
