A scrappy and forgettable first half was punctuated by Ben Davies' 40th-minute opener from close range for Derby, who were without a victory of any kind in seven attempts going into the game.
Blues boss Lee Clark turned to Thomas and Redmond at half-time in a bid to insert some much-needed spark into his side and it paid dividends. After Callum Reilly had rattled the crossbar, on-loan Bournemouth striker Thomas found the net for the first time since his January switch to St Andrew's with a well-taken turn and strike.
But Redmond's goal was the pick of the day as he attacked space before letting fly into the bottom corner from distance, clinching only a second win in seven attempts before Thomas grabbed his second of the afternoon in injury time.
Nikola Zigic enjoyed the first chance of the encounter after 16 minutes but his header from Paul Caddis' cross went narrowly wide of a post.
Davies fired off target from the left channel before the midfielder tested Jack Butland with a 30-yard free-kick after 27 minutes, the first shot of the afternoon to have found the target.
The 15,850 present were finally roused in the 36th minute as Butland dived superbly to tip Chris Martin's long-range effort around a post. And it was not long before the Rams opened the scoring, Davies converting Craig Forsyth's headed ball across the box from close range.
Conor Sammon shot just over before Paul Robinson was called upon to produce a great block to deny the lively Martin a surefire second. Adam Legzdins saved from Zigic's header just before the break as Blues went into the interval behind.
Clark made a double change at the break, introducing Thomas and Redmond, and the changes contributed to a more open second period, Reilly striking the crossbar from 25 yards on the hour mark.
Zigic nodded over the bar from Shane Ferguson's cross as the home side stepped up the pressure, and the goal finally came in the 67th minute. Fellow sub Ravel Morrison found Thomas and he turned well from 18 yards to fire past Legzdins.
The clash was turned on its head minutes later as Redmond drove into space and fired low into the bottom corner with his left foot from more than 25 yards.
Butland did well to parry from Jake Buxton as the Rams went in search of a leveller, defender Richard Keogh then headed narrowly wide before the visitors appealed for a penalty as Sammon collided with Butland. But Thomas settled matters in injury time with his second of the afternoon from 12 yards.