With 14 minutes remaining Miller missed a golden chance to seal the points, diverting a perfect pass from Davis high over Cerny's bar from eight 10 yards.
Having done well to control a clipped pass from Steve Davis, Miller blasted over the bar in three minutes when DaMarcus Beasley was in a more advantageous position.
Eastlands was emptying out by the time City launched a late rally, Adebayor almost latching on to a Silva pass and Fabianski tipping Boateng's drive over the bar.