Eddie Howe's in-form Clarets were on the back foot for long periods as City controlled possession astutely but failed to find a cutting edge.
They paid the price after 34 minutes when defender Jack Hobbs and goalkeeper Peter Gulacsi left a clearance for one another and Paterson benefited from the ensuing panic.
In the moments leading up to the winning goal Hobbs and Aaron McLean might have put Hull ahead, while caretaker boss Nicky Barmby watched on in frustration as Robert Koren passed up a pair of clear openings in the second half.
Victory moves Burnley up to seventh in the table, three points behind sixth-placed Hull.
Brian Easton replaced hamstring injury victim Michael Duff in the Burnley defence, while winger Keith Treacy was preferred to Junior Stanislas.
Paul McShane replaced the suspended Liam Rosenior in Hull's only change.
Matt Fryatt had an early opportunity for the visitors, engineering space in the area after collecting a pass from McLean, but Burnley goalkeeper Lee Grant held his shot.
Koren was the outstanding player in the game's opening moments as Hull settled well and a last-ditch tackle from Easton was required to thwart the Slovenian playmaker.
Burnley's top scorer Jay Rodriguez had the ball in the net from close range shortly before the half hour, but David Edgar's flick on was adjudged to have come from an offside position.
Hobbs should have given Hull a 31st minute lead after marauding forward from the centre back, feeding the ball to Andy Dawson and continuing his run to meet the full-back's subsequent cross, only to drill wide from 12 yards.
McLean passed up an even better opening moments later, making poor headed contact when he Corry Evans' centre found him unmarked in the Burnley area.
Hull were made to pay for their profligacy when Paterson raced towards a long clearance from Grant and capitalised on some costly hesitation from Hobbs and Gulacsi to stoke into an unguarded net.
Barmby's men looked for an instant response as McLean combined with Evans before fizzing a dangerous ball across the face of goal and Dawson burst into the box to shoot wide as Grant narrowed the angle.
With his costly error fresh in the memory, Gulacsi hobbled out of the action shortly before the interval to be replaced by Adriano Basso.
Howe switched to a 4-5-1 formation at the start of the second half, but Hull continued to control the midfield and Koren passed up a gilt-edged chance in the 54th minute, slashing wide of the far post left-footed after Dawson found him in space.
Another chance came Koren's way midway through the half, but he fired over from McLean's cross.
As Hull continued to commit men forward the Clarets had the opportunity to seal the points on the counter-attack, with Wallace picking out Paterson and Basso produced an impressive stop.
Rodriguez spurned another chance on the break to leave the home fans sweating in stoppage time as Edgar headed dangerously towards his own goal, but Grant held on.