Scott Hogan scored the opening goal of the match in the 31st minute and Jeremie Bela added a second in the 81st minute as the Blues won for the second time in their last three matches.
The Rams are now winless in three and remain 15th in the table.
Story of the match
The game started out as an open affair and in the sixth minute, Tom Lawrence saw the ball arrive at him quickly before a low effort was pounced on by Matija Sarkic.
At the other end a Jeremie Bela cross was deflected into the path of Ivan Sunjic and he unleashed a powerful shot that was charged down by the Derby defense.
The hosts were nearly in front when Harlee Dean headed a long throw from Marc Roberts that was shot wide by Hogan.
The ball was lifted back into the area and Roos got a touch on it, but right into the path of Hogan, who hooked it over the line to give Birmingham the lead.
The lead was almost doubled after a slip in the Rams defense saw Roos' short pass fall directly to Hogan, but his first-time shot was wide of the left-hand post.
A minute into the second half, Bela got past his marker and latched onto the end of a deep cross from Tahith Chong, but he turned it just wide.
On the hour mark, Chong glided in from the left and delivered another cross that Buchanan turned behind for a corner, which came to nothing.
Lawrence turned the ball on his left foot and blistered a shot that Surkic turned away and Louie Sibley sent the rebound over the bar.
A Buchanan cross was tipped over by Sarkic and Roos gathered in a long throw by Roberts on the second attempt.
Soon after, Birmingham doubled their advantage nine minutes from time as the Blues forced a turnover Sunjic squared for Bela and despite pressure by Sibley, he took a touch and rifled past Roos to make it 2-0.
There were no more meaningful action as Birmingham move into the play-off places.
Man of the match: Tahith Chong
He shined throughout, providing several fine crosses to set up his teammates for quality chances. Birmnigham have found a real gem in the Dutchman.