MD88 with ZDC at FL330 experienced TCAS RA with unreported traffic; ATC indicated failed intrafacility coordination caused event; legal separation was maintained due to pilot action.

Narrative

Night TCAS RA. At cruise at FL330; we received a traffic alert from TCAS which immediately transitioned to an RA. Traffic was first observed on the radar screen 5 NM ahead and 500 FT below us and in a climb (we could also see it visually). TCAS directed a descent and I disconnected the autopilot and started down. We notified ATC about the traffic and the RA and they instructed us to 'do whatever you need to do...turn right if you can.' We leveled off at about FL324 when we were clear of conflict and climbed back up to FL330. I was given a phone number for ZDC which I called upon landing. The Supervisor told me that the incident was under investigation but it appeared that the other aircraft (southbound) had been cleared to climb through our altitude from FL320 to FL340 by the previous Controller and was not yet talking to our Controller. He said that it looked like on the radar tracks that we 'did a heck of a job' turning a really bad situation into an OK one. He also commented that because of my maneuver; there was not a loss of separation. I do not know how close we came to each other.