Palace, who went into the game without a victory in five, took the lead in the 14th minute through the impressive Wilfried Zaha, his first goal since October.
Stephen Pearson hit the bar for the Robins 10 minutes before half-time before Palace doubled their advantage with 21 minutes remaining.
Darren Ambrose converted from the penalty spot after Glenn Murray was fouled by Liam Fontaine, the midfielder scoring his first goal since his stunning effort in the Carling Cup win over Manchester United at Old Trafford in November.
The Robins pulled a goal back in the 77th minute when Pitman, who had only been on the pitch for seven minutes, struck home a 25-yard free-kick, his first goal in 13 matches.
Pitman then added a second three minutes into injury time, slashing home from 18 yards after a long ball into the box.
Palace, whose home clash with Doncaster on Saturday fell foul of the weather, made a bright start and Zaha forced Robins goalkeeper David James into a save inside five minutes.
The home side responded but Yannick Bolasie blasted high and wide from 35 yards.
Bolasie was closer with his next effort moments later, this time failing to direct his header from Albert Adomah's cross on target from the edge of the area.
But Palace took the lead in the 14th minute when Zaha cut inside before unleashing a shot into the top corner from 18 yards.
City levelled almost immediately, but Palace goalkeeper Julian Speroni did well to parry Chris Wood's close-range header.
Opportunities kept coming for both sides and this time it was City's turn to go close. Patrick McCarthy was penalised for a foul on Wood and from the resulting free-kick Adomah failed to keep his shot down.
Jermaine Easter pulled his effort wide before the Robins started to up the ante, with Marvin Elliott having his 25-yard strike saved by Speroni before a 30-yard blast from Pearson crashed against the bar.
Pearson attempted to go one better moments into the second half, but could not keep his 20-yard shot on target.
Speroni then denied Adomah from 12 yards as the Robins continued to search for the equaliser.
Eagles striker Chris Martin was thwarted by Speroni and James was also in fine form at the other end to deny Zaha before the visitors made it 2-0 with Ambrose converting from the spot.
The Robins pulled a goal back with Pitman firing home a 25-yard free-kick and they nearly levelled in the last minute, but Speroni superbly tipped Wood's header over the bar.
However, the hosts were not to be denied as Pitman pounced to salvage a point.