It had looked like Neil Danns' second-minute free-kick would give Palace only their second away win of the season in the npower Championship.
However, Julian Speroni brought down Danny Rose and Pitman converted the 94th-minute spot-kick.
City boss Keith Millen made five changes following the heavy Boxing Day defeat to Reading.
Two were enforced with Jamie McAllister and Christian Ribeiro injured at the Madejski Stadium, while Damion Stewart, Rose and Pitman dropped down to the bench.
Lewin Nyatanga, Kalifa Cisse, Lee Johnson, Jamal Campbell-Ryce and Danny Haynes came into the side.
This was the first time Palace had played since a 3-0 defeat at Nottingham Forest on December 18 but boss George Burley also rang the changes.
Like City, two were enforced with Darren Ambrose and Owen Garvan injured. Andy Dorman and Alassane N'Diaye had to settle for a place among the substitutes as Wilfried Zaha, Julian Bennett, Calvin Andrew and Sean Scannell were recalled.
Danns gave Palace the perfect start. The midfielder was pulled down by Cisse on the edge of the area, he got up and beat David James all ends up with his shot finding the top right-hand corner.
Haynes almost headed an immediate reply but his effort struck a post before Albert Adomah shot just wide soon afterwards.
Danns missed with a couple of long-range efforts before forcing James to tip a shot over the bar just after the half-hour mark.
Back at the other end, Johnson and Adomah went close before the break.
Palace should have gone 2-0 up when Pablo Counago played a neat one-two with Scannell but the Spaniard put his shot wide.
Millen responded by boosting his firepower with the introduction of Pitman, Rose and David Clarkson, but City struggled to create chances in the second half.
Rose had an effort blocked after 77 minutes but it was not until the 85th minute that Palace keeper Speroni was called into action to tip over a shot from Adomah.
Speroni then conceded the penalty and was unable to make amends.