The striker netted with a brilliant 25-yard curling effort in the 74th minute to ensure a share of the spoils for the Robins, who are now winless in five matches.
City started well but fell behind against the run of play in the 20th minute when Craig Bryson slotted home from Jeff Hendrick's pass.
Steve Davies thought he had doubled the Rams' advantage 10 minutes before the break but the forward's header was disallowed for offside.
After half-time, Albert Adomah headed narrowly over from Cole Skuse's cross before Davies again went close for the visitors - this time the striker crashed a shot against a post from a tight angle.
It seemed the hosts would slip to their third successive home defeat, but with 16 minutes remaining the Robins levelled through Pitman's spectacular effort.
Skuse replaced the suspended Ryan McGivern in defence for City, while Derby manager Nigel Clough named an unchanged side following the Rams' 3-2 victory over Crystal Palace last time out.
The home side created the first chance of the match after four minutes, but Adomah's 18-yard drive was comfortably caught by Frank Fielding in the Derby goal.
Ricky Foster then fired narrowly wide from the edge of the area as City took control of the game early on. But they were hit by a sucker-punch midway through the first half as Derby took the lead with their first real attack.
Hendrick timed his run perfectly to beat the offside trap down the left and composed himself well to square for Bryson, who produced a clinical side-footed finish to beat Dean Gerken in the hosts' goal.
City rallied and were upset not to be awarded a penalty when Jon Stead's goalbound effort appeared to strike Paul Green on the arm, but referee Gavin Ward waved away the home side's appeals.
Adomah's tame effort could not trouble Fielding, while Davies fired well wide for the visitors before the forward had the ball in the back of the net for the Rams, only for the strike to be ruled out for offside.
After going into the interval behind, City started well after the break and Adomah nodded Skuse's cross over the crossbar from six yards out.
But the hosts failed to build on their early momentum and were fortunate not find themselves further behind when Davies found space in the box to rattle a post from a narrow angle.
And City made the most of their good fortune to level in the 74th minute.
Adomah slipped the ball to substitute Pitman 20 yards out and the striker fired a superb right-footed finish beyond Fielding.
City goalkeeper Gerken produced a good save to deny Hendrick with time running out, and it proved crucial as the home side held out for a point.