The visitor's made the perfect start with Krystian Bielik finding the net, and Graeme Shinnie bagging a penalty in quick succession.
Colin Kazim-Richards scored his third goal of the season to give Derby a three-goal lead at the break.
Birmingham didn't show much more life in the second half though, as Derby stood firm and took advantage again with Jason Knight seeing them off, as Derby took all three points.
Story of the match
Derby County's form has indeed improved under the tenure of Wayne Rooney, after a first loss came for the Rams interim boss at the weekend at home to Preston North End, they were desperate to get back to winning ways at St Andrew's.
For Birmingham City, it's been a torrid few weeks after being winless in their last four games, and knowing they hadn't beaten Derby since January 2016, a tough task was ahead of the blues tonight.
Inside the first five minutes the game was rather end to end, something many didn't expect to see from two teams who've been lacking goals. Louie Sibley went close for Derby and an effort from Ivan Sanchez for Birmingham was deflected wide.
The first goal came on the 15th minute though and it was a rare mistake from Birmingham goalkeeper Neil Etheridge. As Shinnie whipped the ball into the box, it should've been an easy catch for Etheridge, but as he goes to gather, he fumbles the ball out of his hands into the feet of Bielik, who poked the ball into the net to find his first goal for Derby County, against his former club.
One minute later and a mountain of misery came for the Blues. A sloppy challenge from Harlee Dean as he tripped up Sibley, the referee had no hesitation and pointed to the spot. Shinnie made no mistake and buried his penalty into the corner, Etheridge was fingertips away from making a fabulous stop.
25 minutes in, and Rooney's Ram's made it three. A calamity in the box as Shinnie whipped in another corner, which was flicked on by Matthew Clarke, which then caught the head of Birmingham midfielder Gary Gardner, to then land in the feet of Colin Kazim-Richards who slotted into an empty net, two-yards out.
Derby were dominating. The Rams took advantage on set pieces, with seven corners in the first half, they provided a chance at every opportunity, just before half-time it was lucky not to be four.
Matthew Clarke's header was stopped off the line from Adam Clayton, who knocked it out for another corner. Shinnie with his lethal left foot, whipped in another beauty, to the head of Clarke again, who's header went straight into the hands of Etheridge.
Birmingham boss Aitor Karanka tried everything in his power to boost his side into life, as over the half-time period he was forced into making four changes.
It went bad to worse for Birmingham as on the 59th minute, Gardner went down with a potential pulled hamstring and the Blues were forced into their fifth and final change with 30 minutes still left to play.
A quarter of an hour left on the clock, and County made it four. A tricky performance from winger Kamil Jozwiak, as his delightful cross found Jason Knight at the back post to pop up and slot the ball into the net to find his first league of the season for Derby.
The changes for Karanka certainly didn't go as he planned. It took the blues till the 85th minute to register a shot on target as Jutkiewicz came close.
Man of the match
A few contenders for Derby County as the performances were impressive all round.
Taking the award tonight though is Graeme Shinnie. His performance was dominant in the midfield and he didn't step a foot wrong. His set pieces were consistently dangerous and he found the scoresheet with a goal from the penalty spot.