Miller capitalised on a moment of casual defending by Birmingham centre-back Pablo Ibanez to fire beneath Boaz Myhill after 68 minutes to fire home his ninth goal of the season and give the Bluebirds their sixth consecutive home win.
Just five minutes earlier the visiting Blues had been reduced to 10 men following the dismissal of Curtis Davies after he brought down Miller when clean through.
Up until that point Cardiff had been forced to play the majority of the game in front of two lines of Birmingham defence, and both sides struggled to create golden opportunities.
But the red card changed the match in the home side’s favour, and Cardiff dominated the majority of the final quarter.
Peter Whittingham hit a post with a rasping free-kick, before firing inches wide from the edge of the box, as the Welsh outfit climbed back into third place.
Miller had the first chance of the game for Cardiff, heading wide from 12 yards following Lee Naylor’s cross from the left after four minutes, as the hosts enjoyed the majority of the possession in the early stages.
Birmingham took 10 minutes to mount their first serious attack into Cardiff territory, and even then Nikola Zigic was unable to direct his header from Marlon King’s centre on target.
At the other end Aron Gunnarsson lashed high and wide from distance for the Bluebirds, as both teams struggled to create anything close to a clear-cut sight of goal.
Passes were going astray with frustrating regularity, and the midfield pinball continued until the 34th minute, when Cardiff finally carved out the game’s first effort on target.
Unsurprisingly perhaps the in-form Whittingham was the perpetrator, receiving Kevin McNaughton’s pass on the edge of the area and cutting inside onto his left foot before unleashing a low drive which was saved by Myhill in the Birmingham goal.
Buoyed by their first real sight of goal, the home side were on the attack minutes later. However, an off-balance Filip Kiss could only clear Myhill’s bar from range.
Birmingham saw little of their opponents’ penalty area throughout the first half, and Zigic wasted their best chance just before the break.
Chris Burke delivered a corner from the right, and the tall Serbian should have done better than nod over from 10 yards out.
Moments after the interval, Zigic had an even more gilt-edged opportunity to put the Blues ahead.
Seizing on a fortunate bounce, the striker galloped into the area and had all the time in the world to beat David Marshall in the Bluebirds goal.
Bizarrely, however, Zigic decided to centre for the double-marked King, and his errant pass was easily cleared.
The second half started infinitely more lively than the first. Whittingham fired over when well set for Cardiff after 49 minutes and Burke nodded straight at Marshall at the other end before the match’s first major flashpoint on 63 minutes.
Miller, played clean through on goal, fell under the challenge of Davies on the edge of the box.
Last man Davies saw red, cueing a furious reaction from the Birmingham players, and Whittingham rifled the resulting free-kick against Myhill’s right-hand post with the keeper beaten.
Cardiff soon made their one-man advantage count, however, although their cause was helped by a moment of seasonal generosity from Birmingham centre-back Pablo Ibanez.
Ibanez, perhaps exhibiting the Christmas spirit three weeks prematurely, tamely nodded Craig Conway’s cross into the ground and straight to the feet of Miller.
Unmarked, the Scot had little else to do but pick his spot beyond Marshall, which he did with aplomb.
Suddenly the hosts were dominant. Whittingham fizzed an effort from 18 yards narrowly past the post and curled another attempt well over as somehow the Bluebirds failed to score a second before the final whistle.