Lukas Jutkiewicz scored a controversial second-half penalty as Coventry recorded their first win of the season and moved out of the Championship relegation zone.
Jutkiewicz struck after Jason Shackell was harshly adjudged to have impeded Richard Keogh.
Carl Baker sealed the win with a superb volley to condemn Nigel Clough's County to a second straight defeat.
Derby forward Steve Davies missed the Rams' best chance.
The Sky Blues had failed to score in either of their previous games at the Ricoh this season and, in a fairly uneventful first half, rarely threatened Fielding's goal.
Left-back Chris Hussey hit a speculative long-range effort from the left that the County keeper comfortably caught but it was the visitors who looked most likely to make a breakthrough as the first half drew to a close.
Injured Coventry keeper Murphy was replaced by Chris Dunn at the interval and Dunn was immediately called into action to deny John Brayford's attempt from the edge of the area.
Jutkiewicz then turned Cyrus Christie's cross narrowly wide before the home side's early second-half pressure eventually paid off just before the hour mark, albeit in controversial fashion.
Clingan curled a corner in from the Coventry left and after Rams defender Shackell collided innocuously with Keogh, Jutkiewicz stepped up to send Fielding the wrong way from the spot.
Andy Thorn's men continued to press and substitute Roy O'Donovan stung the palms of Fielding before Baker put them in complete control with 11 minutes left.
Christie sent in a long-throw from the right-hand side and the Derby defence could only flick the ball on to midfielder Baker, who smashed home from close range.