Antti Niemi's heroics earned a point for 10-man Fulham as Derby dominated the home side at Craven Cottage.
Fulham's Seol Ki-Hyeon after a first-half miss against Derby
Niemi denied Kenny Miller and Giles Barnes twice each and even saved well from his own defender Aaron Hughes.
Fulham's Paul Konchesky was sent off in first-half injury time for elbowing Craig Fagan, but Lawrie Sanchez's side somehow survived for a draw.
Miller was off target in injury time, while Craig Dempsey forced two saves from Derby keeper Stephen Bywater.
In a game of dubious quality, Fulham keeper Niemi stood between Derby and the crucial breakthrough that would have given them their first away win of the season.
Fulham look a poor side, despite the money spent by Sanchez, and it needed Niemi to be at his best to keep Derby at bay.
He did well to save from Miller then produced a fine reaction save to stop a header from his own defender Hughes in the 33rd minute as he dived to divert Stephen Pearson's cross.
Derby were forced into a change two minutes before half-time when Barnes came on to replace the limping Claude Davis.
But Fulham suffered a bigger blow in first-half injury time when Koncheskey was sent off for raising his hands to Fagan as they tussled on the flank.
Dempsey was one of the few Fulham threats, having a shot saved, then seeing a header turned over by Derby keeper Bywater.
But Niemi was still the star of the show, saving Barnes' header with his feet and then blocking a drive at the near post.
He rescued Fulham again with 14 minutes to go as Miller raced clear, diving low to turn away his shot as he looked poised to score.
Fulham were attempting to make the most of their good fortune, and Diomansy Kamara tested Bywater after a mazy run.
How Derby had failed to claim the three points was a mystery, and even in injury time Miller finally beat Niemi but the ball rolled agonisingly wide.
Fulham manager Lawrie Sanchez on Konchesky's sending off:
"I don't think there was any argument to be fair. Paul has been our best player this season but the referee had no other option.
"I will have a word with the lad on Monday and see what it is about because it seems out of character in terms of the game. I saw it 50 yards away and knew the referee had no option.
"We will deal with it internally but it is disappointing. We played poorly in the first half, we looked tentative, nervous, and waiting for something to go wrong.
"So then we do something wrong by going down to 10 men but I thought we came out and were the better team in the second half."
Derby boss Billy Davies:
"As long as performances are improving and as long as the club can see positive signs, we can ask no more. We are getting better. The players have worked very hard for me.
"The first point away from home is always nice. But we have just got to keep working away because it is a marathon.
"The big warning sign was there at half-time to the players because 10-men is not easy to play against. But I thought we put in a lot of good performances and created a lot of chances.
"I am delighted with the spirit and effort of the players. I am very confident with the people that we've got, that we can consolidate ourselves in the Premier League."
Fulham: Niemi, Baird, Stefanovic, Hughes, Konchesky, Bouazza, Davis (Davies 69), Murphy, Ki-Hyeon (Bocanegra 46), Kamara (Healy 87), Dempsey.
Subs Not Used: Warner, Smertin.
Sent Off: Konchesky (45).
Derby: Bywater, Mears, Moore, Davis (Barnes 43), McEveley (Griffin 71), Pearson, Oakley, Leacock (Howard 78), Lewis, Fagan, Miller.
Subs Not Used: Jones, Earnshaw.
Booked: Leacock, Fagan.
Ref: Phil Dowd (Staffordshire).