A second-half strike from Darren Ambrose gave Crystal Palace their first home league win of the season.
Ambrose's decisive intervention came when he drove home a Shaun Derry header from the edge of the six-yard box.
Johannes Ertl almost stretched Palace's lead when he shuddered the bar with a header, while Rob Hulse missed a chance to level for Derby from 12 yards out.
Palace goalkeeper Julian Speroni escaped with only a yellow card after handling outside the area early on.
Crystal Palace manager Neil Warnock:
"All the talking (Clough on the penalty call) is trying to cover the cracks. Look at their bench. They've got a better side there than we have been able to put out. Let's complain about that.
"I didn't see it like the ref. It couldn't have been a foul or else he would have given it.
"We gave absolutely everything and I'm proud as punch of my boys and I hope they get the headlines they deserve."
Derby manager Nigel Clough:
"I thought we created the two best chances of the game and thought we had an absolute blatant penalty in the 92nd minute.
"Anywhere else on the pitch, a late tackle on Kris Commons, and he the referee gives a foul.
"When you have seen a player taken off on a stretcher after he's had a shot, I don't think there's any argument that that can be a fair challenge."
90:00+4:30 Inswinging corner taken by Gary Teale, clearance made by Clint Hill.
90:00+1:09 Kris Commons takes a shot. Save made by Julian Speroni.
90:00+0:50 Neil Danns takes a shot. Save made by Stephen Bywater.
88:19 Johannes Ertl has an effort at goal from deep inside the area missing to the right of the goal.
86:43 Free kick taken by Julian Speroni.
86:43 Substitution Nick Carle joins the action as a substitute, replacing Sean Scannell.
86:43 Rob Hulse concedes a free kick for a foul on Patrick McCarthy.
85:59 Unfair challenge on Stephen Pearson by Shaun Derry results in a free kick. Stephen Pearson restarts play with the free kick.
81:20 Unfair challenge on Rob Hulse by Jose Fonte results in a free kick. Gary Teale delivers the ball from the free kick left-footed from left channel. Lee Croft takes the inswinging corner, Rob Hulse takes a shot. Save made by Julian Speroni.
80:55 Free kick awarded for an unfair challenge on Robbie Savage by Sean Scannell. Stephen Bywater restarts play with the free kick.
79:58 Substitution Kris Commons is brought on as a substitute for Miles Addison.
79:11 Sean Scannell takes a shot. Blocked by Paul Connolly. Inswinging corner taken by Darren Ambrose, clearance made by Paul Connolly.
77:40 Substitution (Derby) makes a substitution, with Shaun Barker coming on for Dean Leacock.
76:11 Darren Ambrose takes a shot. Stephen Bywater makes a save.
73:52 Jose Fonte gives away a free kick for an unfair challenge on Rob Hulse. Direct effort from the free kick comes in from Gary Teale.
72:51 Jose Fonte fouled by Rob Hulse, the ref awards a free kick. Free kick taken by Jose Fonte.
72:19 Effort on goal by Rob Hulse from inside the penalty box misses to the right of the target.
70:10 Unfair challenge on Neil Danns by Paul Connolly results in a free kick. Free kick taken by Jose Fonte.
68:37 James Vaughan challenges Danny Butterfield unfairly and gives away a free kick. Darren Ambrose crosses the ball, Johannes Ertl takes a shot.
66:19 Substitution Stephen Pearson joins the action as a substitute, replacing Jake Livermore.
66:09 James Vaughan concedes a free kick for a foul on Patrick McCarthy. Julian Speroni takes the indirect free kick.
65:40 The referee penalises Sean Scannell for handball. Stephen Bywater takes the free kick.
64:45 Free kick awarded for a foul by Alan Lee on Dean Moxey. Dean Moxey crosses the ball from the free kick right-footed from left wing, save by Julian Speroni.
61:52 The assistant referee signals for offside against James Vaughan. Julian Speroni takes the indirect free kick.
58:47 The free kick is delivered right-footed by Clint Hill from left channel, Lee Croft manages to make a clearance.
58:47 Booking Lee Croft goes into the book.
58:28 Free kick awarded for a foul by Lee Croft on Sean Scannell.
57:47 Free kick awarded for a foul by Patrick McCarthy on James Vaughan. The free kick is swung in right-footed by Gary Teale, Shaun Derry makes a clearance.
Correction - 54:26 Shaun Derry provided the assist for the goal.
54:26 The assist for the goal came from Sean Scannell.
54:26 GOAL - Darren Ambrose:Crystal Palace 1 - 0 Derby Darren Ambrose scores a goal from the edge of the area to the bottom right corner of the goal. Crystal Palace 1-0 Derby.
53:31 Corner taken left-footed by Darren Ambrose to the near post, Paul Connolly manages to make a clearance.
52:49 Gary Teale has an effort at goal from the edge of the area that misses to the right of the target.
51:43 Unfair challenge on Dean Moxey by Sean Scannell results in a free kick. Stephen Bywater restarts play with the free kick.
50:57 Inswinging corner taken from the right by-line by Lee Croft.
50:11 Lee Croft takes the inswinging corner, Clint Hill manages to make a clearance.
46:51 Dean Leacock gives away a free kick for an unfair challenge on Alan Lee. The free kick is delivered right-footed by Darren Ambrose from right channel. Clint Hill is flagged offside by the assistant referee. Stephen Bywater takes the free kick.
45:01 The match restarts for the second half.
Half Time
45:00+2:06 The ref blows to signal half-time.
45:00+1:00 Free kick awarded for an unfair challenge on Miles Addison by Alan Lee. Indirect free kick taken by Stephen Bywater.
44:39 Alan Lee gives away a free kick for an unfair challenge on Miles Addison. Free kick taken by Stephen Bywater.
39:37 Gary Teale crosses the ball from the free kick right-footed from right wing.
39:37 Booking Patrick McCarthy receives a yellow card for unsporting behaviour.
39:29 Lee Croft fouled by Patrick McCarthy, the ref awards a free kick.
38:37 Alan Lee takes a shot. Stephen Bywater makes a fantastic save.
37:31 Darren Ambrose takes a shot from inside the six-yard box clearing the crossbar.
35:46 Free kick awarded for an unfair challenge on Alan Lee by Dean Leacock. The free kick is swung in right-footed by Danny Butterfield, clearance by Paul Connolly.
35:19 Neil Danns produces a volleyed right-footed shot from 35 yards. Save by Stephen Bywater.
34:41 Sean Scannell is caught offside. Indirect free kick taken by Stephen Bywater.
34:28 Johannes Ertl takes a shot. Stephen Bywater makes a save.
31:23 The offside flag is raised against Rob Hulse. Indirect free kick taken by Julian Speroni.
29:29 Shot from 35 yards by Neil Danns missed to the right of the net.
25:24 Darren Ambrose takes a corner.
24:01 Jake Livermore takes a shot. Julian Speroni makes a save. Inswinging corner taken by Lee Croft from the right by-line, Clint Hill manages to make a clearance.
23:15 The assistant referee flags for offside against Neil Danns. Free kick taken by Stephen Bywater.
22:01 The referee blows for offside against Rob Hulse. Julian Speroni takes the indirect free kick.
19:02 The referee penalises Julian Speroni for handball. Gary Teale delivers the ball from the free kick right-footed from left channel, save made by Julian Speroni. Corner from the right by-line taken by Lee Croft, Alan Lee makes a clearance.
18:30 Booking Julian Speroni receives a yellow card.
15:34 The free kick is swung in right-footed by Jose Fonte, clearance made by Miles Addison.
15:34 Booking Jake Livermore is given a yellow card.
15:22 Free kick awarded for an unfair challenge on Darren Ambrose by Jake Livermore.
14:25 Corner from the left by-line taken by Darren Ambrose, clearance made by Dean Leacock.
Correction - 11:04 Unfair challenge on Clint Hill by Rob Hulse results in a free kick. Julian Speroni takes the indirect free kick.
11:04 Clint Hill fouled by Rob Hulse, the ref awards a free kick. Indirect free kick taken by Julian Speroni,
9:04 Shot from deep inside the area by James Vaughan clears the crossbar.
7:06 Shaun Derry gives away a free kick for an unfair challenge on Jake Livermore. Robbie Savage crosses the ball from the free kick right-footed from right channel.
4:08 Johannes Ertl has an effort at goal from outside the box which goes wide right of the target.
3:29 The offside flag is raised against James Vaughan. Julian Speroni takes the indirect free kick.
3:05 The referee blows for offside against Alan Lee. Stephen Bywater takes the free kick.
2:04 Foul by Shaun Derry on Rob Hulse, free kick awarded. Dean Moxey delivers the ball from the free kick right-footed from left channel, save by Julian Speroni.
0:30 Unfair challenge on Patrick McCarthy by James Vaughan results in a free kick. Direct free kick taken by Clint Hill.
0:00 The game begins.
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