Birmingham were behind at half-time in the St Andrew's tussle, but in the second 45 minutes they were a changed side.
Clark brought on both Thomas and Redmond for the start of the second half in what turned out to be an inspired step.
Thomas netted twice and Redmond scored his long-awaited first of the season as Birmingham won at home for only the sixth time this season to ease relegation fears.
Clark said: "Even thought there was not too much difference in the first half I thought that Derby were gaining momentum by each minute and the game was there to be taken if we wanted it.
"Derby have a lot of energy and a great work ethic and we had to match that if we were to get anything from the game.
"They were more energetic than us in the first half and I decided to get the two lads on with a bit of power and pace. I am delighted for both of them."
- Sports & Recreation