Buckley was back in the mix of things again and his cross from the left found the head of Leo Ulloa from six yards, but again Randolph got down low to make a fine save to keep the scores level.
Brighton should have gone one ahead minutes later when Ulloa beat the offside trap but he finished poorly, the ball going wide of Randolph's goal.
City came out of the traps quickest in the second half and should have taken the lead when Shinnie let fly only to see his shot rattle the crossbar following a good buildup play from Allan.
Birmingham fans had their heads in their hands again only a few minutes later when Novak took his turn to hit the bar with a powerful strike from 18 yards.
It did not take too long for Brighton to respond and they would have gone ahead had it not been for a fine save from Randolph, who kept out Kemy Agustien's powerful shot from just inside the box.
Birmingham continued to attack but they were stung against the run of play when Andy Crofts thumped in a low shot from 12 yards to give Brighton a 1-0 lead.