Pitman opened his account for City three weeks ago against Leicester and followed that up with a brace against Sheffield United to help Keith Millen's side to successive wins for the first time this season.
The former Bournemouth striker netted another double against the Rams to get on the scoresheet for the third consecutive game.
His first came early in the second half when he got on the end of Albert Adomah's cross. Adomah was the architect again in the 68th minute, sliding the ball through for Pitman to beat Stephen Bywater.
It saw City extend their record to only one defeat in the last nine matches, while Derby's slump continued with a fourth defeat in five league games.
Rams boss Nigel Clough will point to an incident at the end of the first half involving David James that might have turned the game in his side's favour.
The former England keeper brought down Kris Commons when Derby's leading scorer was through one-on-one. Referee Darren Sheldrake deemed the offence only worthy of a yellow card, but James should really have been sent off.
City created all the meaningful first half chances. The first came after just 38 seconds when Marvin Elliott headed over Pitman's cross.
Jamie McAllister's inswinging free-kick clipped a post before Pitman had a volley saved by Bywater, who was making his return from a wrist fracture.
Clough was then incensed by the incident involving James, and his mood would not have improved when Derby fell behind just three minutes after the restart.
Adomah put the ball across the face of goal from the right side and Pitman tapped in at the far post.
Derby dominated thereafter but only forced James into action on one occasion when Commons' 12-yard shot was tipped over the crossbar. Shaun Barker headed wide and Paul Green had an effort blocked by Damion Stewart.
It was against the run of play when Pitman struck for the second time.
The goal came from the right with Adomah once more involved. His pass put Pitman clear and he beat Bywater from just inside the area.
Derby were deflated but Commons continued to look threatening. The Scotland international narrowly missed with a long-range shot and had another effort saved by James.
Bywater blocked a close-range effort from Steven Caulker late in the game to prevent a heavier defeat for the Rams.