Match ends, Birmingham City 0, Derby County 4.
Birmingham City suffered a defensive nightmare at St Andrew's as grateful Derby County romped to their best win under Wayne Rooney.
Blues shipped three goals inside the first 25 minutes as Rooney's Rams bounced back from losing at home to Preston on Saturday - their first defeat since the Derby caretaker boss took sole charge.
Former Blues defender Krystian Bielik cashed in on home keeper Neil Etheridge's dropped clanger in the 15th minute to volley in from close range.
Inside two minutes, home captain Harlee Dean gave away a needless penalty, which was clinically tucked away by Graeme Shinnie.
Blues then let in a third when they made a shambles of clearing Shinnie's corner, allowing Colin Kazim-Richards to net from close range.
Youngster Jason Knight completed the scoring after 77 minutes when he neatly tucked away Kamil Jozwiak's right-wing cross.
It was Derby's biggest away league win since a 4-0 win at the same venue for Steve McClaren's team against Gary Rowett's Blues on Boxing Day 2014.
Derby move out of the Championship's bottom three for the first time in two months after stretching their unbeaten run in this fixture to nine matches.
Blues, who had also conceded four goals in their previous home game against Middlesbrough, had responded well with a clean sheet on Saturday at Nottingham Forest, another of boss Aitor Karanka's former clubs.
But any hopes of a repeat evaporated from the moment Etheridge committed his howler, allowing the ball to bounce tamely off his chest as he rose unmarked to gather Shinnie's right-wing corner.
Bielik was first to respond, lashing in a right-foot volley from 10 yards to mark his first goal for the club. And worse was to follow for the hosts.
Dean was in no danger on the right edge of the Blues box but his clumsy challenge on Louie Sibley gave the Derby youngster the chance to go down and Shinnie did the rest, firing a fine penalty.
Then, from another Shinnie corner from the right, the ball deflected off home midfielder Adam Clayton before Kazim-Richards lunged in to get the final touch from a yard.
With the outcome already settled, the Blues added a fourth on 77 minutes when Jozwiak went down the right, cut back inside on to his left foot and curled over a cross. It dipped beyond the Blues defence at the far post, where the alert Knight crept in unmarked to guide home left-footed from close range.
After picking up six points from their first 11 games this season under Philip Cocu, then losing their next two, Derby have now amassed 13 in 10 under Rooney.
Karanka's Blues, by contrast, have picked up just one point out of a possible 15 - and are now just four ahead of Derby, who have a game in hand.
Derby next travel to face managerless Sheffield Wednesday on New Year's Day, while City's next game is at home to Blackburn Rovers the following day.
Birmingham City boss Aitor Karanka:
"It's like going to the cinema and watching the same film. One mistake, one goal. Two mistakes, two goals. Three mistakes, three goals.
"It's difficult to accept but it is something we are suffering. And it's hard to understand when one game you are perfect and the next game you make the same mistakes as a couple of games before.
"I apologise to the fans. But they must keep belief in the team. Three days ago we did well, so why not the same? I expected ups and downs this season, but not these same individual mistakes every single game."
Derby County caretaker boss Wayne Rooney:
"That performance has been coming over the last few weeks. I'm delighted for the players. I'm starting to see a team that believe in themselves. They have been putting in good performances.
"The results have been getting better, and even though we lost against Preston, the performance was excellent. You can see the confidence growing. They deserve that for the work they have put in.
"I'm not worried. We've got a lot of quality and hopefully with a few players coming in January, we can iron out some of the cracks and take us to that next level."
- 3PedersenSubstituted forClarke-Salterat 45'minutes
- 20GardnerSubstituted forKieftenbeldat 61'minutes
- 34SunjicSubstituted forLekoat 45'minutes
- 11BelaSubstituted forSan Joséat 45'minutes
- 9HoganSubstituted forJutkiewiczat 45'minutes
- 19San José
- 38KnightSubstituted forWatsonat 88'minutes
- 4ShinnieSubstituted forGordonat 89'minutes
- 17SibleyBooked at 67minsSubstituted forBirdat 75'minutes
- 13Kazim-RichardsSubstituted forHector-Ingramat 82'minutes
- 6te Wierik
- Tony Harrington
- Shots on Target
Second Half ends, Birmingham City 0, Derby County 4.
Attempt missed. Lukas Jutkiewicz (Birmingham City) left footed shot from the centre of the box is too high. Assisted by Maxime Colin with a headed pass.
Offside, Derby County. Kaide Gordon tries a through ball, but Jahmal Hector-Ingram is caught offside.
Kamil Jozwiak (Derby County) wins a free kick in the attacking half.
Foul by Jonathan Leko (Birmingham City).
Nathan Byrne (Derby County) wins a free kick in the defensive half.
Foul by George Friend (Birmingham City).
Louie Watson (Derby County) wins a free kick in the attacking half.
Foul by Iván Sánchez (Birmingham City).
Substitution, Derby County. Kaide Gordon replaces Graeme Shinnie.
Substitution, Derby County. Louie Watson replaces Jason Knight.
Attempt saved. Lukas Jutkiewicz (Birmingham City) left footed shot from outside the box is saved in the top centre of the goal. Assisted by George Friend.
Krystian Bielik (Derby County) wins a free kick on the right wing.
Foul by Jake Clarke-Salter (Birmingham City).
Substitution, Derby County. Jahmal Hector-Ingram replaces Colin Kazim-Richards.
Offside, Derby County. Craig Forsyth tries a through ball, but Max Bird is caught offside.
Foul by Krystian Bielik (Derby County).
Lukas Jutkiewicz (Birmingham City) wins a free kick in the attacking half.
Goal! Birmingham City 0, Derby County 4. Jason Knight (Derby County) left footed shot from very close range to the centre of the goal. Assisted by Kamil Jozwiak with a cross.