Hull started the evening at the top of the table, but they were below their best for much of the first half and only Harry Maguire's crucial block prevented Cyrus Christie from finishing a fine run with a goal.
Derby eased through the Hull midfield with a fine passing move, and when Andreas Weimann was stopped on his run at goal, the loose ball was fired home by Butterfield.
An early lead was no more than the visitors deserved, but there was more to come from Clement's side as they recovered from a spell on the back foot to double the lead through Butterfield, who picked out the bottom corner with a volley from the edge of the box after Hull could only clear a cross to the midfielder.
Hull had enjoyed plenty of possession in the first half, but they were unable to threaten until Scott Carson was forced to come to the rescue for Derby.
Derby defended well as Hull attempted to ask more questions early in the second half as the three-man central midfield protected the back four impressively.
Carson was alert to the danger when Maloney found the space to curl a shot which needed to be pushed away from the bottom corner.
Maloney was even closer to pulling a goal back just a few moments later when his powerful effort from close range was pushed over by Carson after Derby had failed to react to a loose ball in the box.
Derby were happy to play without the ball for much of the second half as they dropped deep to limit the space on offer to Hull, whose play in attacking areas often left the home supporters frustrated.
Tom Ince could have wrapped up the win in style against his former side when Chris Martin picked him out on the edge of the box, but his half-volley was inches wide as Derby finished the game comfortably to move a point clear of Hull and Brighton & Hove Albion, who host Birmingham City tomorrow.