The Derby boss, who in midweek signed a new lucrative contract, saw his side strengthen their second in the table position and emerge as strong promotion contenders.
Rowett admitted: “What pleased me were the three goals, which were all different. When Johnny Russell scored the first it settled down the team.
“The one thing I cannot say about us is we can cope with the different styles of play. When we play and get the ball down we have enough ability to exploit spaces, as we demonstrated.”
Birmingham displayed a tenacious battling spirit but Derby’s better finishing was the major difference and explained the current positions of the two clubs.
Johnny Russell put the Rams in the driving seat with a fortunate 19th minute goal, Matej Vydra doubled the lead with a second strike after the break, before Andreas Weimann sealed Derby’s sixth win in eight outings four minutes from time.
Rowett continued: “George Thorne and Tom Huddlestone gave us the composure and control in midfield. This proved vital.
“We have now gone 10 games unbeaten away from home and we are playing with real control.
“In some ways it suits away from home when the opposition want to put us under pressure. That leaves one glimmer of space and we have the players to open up any team.
“This is why I’m pleased with the control and management the team displayed.”
Blues boss Steve Cotterill expressed his disappointment with the latest defeat which keeps his side in the bottom three.
He said: “I thought we started the game…