The South African midfielder’s first goal of the season arrived with six minutes left as the Eagles finally found a way past Bo Myhill in the Blues goal.
Chris Hughton’s side arrived in south London looking to kick-start their npower Championship promotion bid after they bowed out of the Europa League last week.
Myhill looked to have ensured that gap would be cut to five with a string of fine saves, while the woodwork denied the Eagles’s Irish skipper Paddy McCarthy.
But Palace were not to be denied and the man known as ‘KG’ conjured up a dramatic late winner for Dougie Freedman’s side.
Palace started sluggishly and Birmingham striker Marlon King will know he should have done better when he volleyed Stephen Carr’s cross over early on. But their ‘keeper Myhill was called into action to tip away Mile Jedinak’s sweetly-struck effort at the other end as the game began to open up.
Jedinak, yet to score for Palace, had another chance when he met Darren Ambrose’s free-kick with a firm header but Myhill dived to his right to make another super save.
And in the 69th minute Eagles skipper McCarthy arrived at the far post to meet Ambrose’s corner but his header crashed back off the foot of the upright.
Birmingham could have nicked a goal as full-time approached when Speroni parried Burke’s angled drive but Caldwell headed the follow-up over the top.
Instead, Dikgacoi had the final say after the visitors failed to clear Ambrose’s corner and the giant midfielder powered his header past Myhill.
CRYSTAL PALACE: Speroni, Clyne, McCarthy, Gardner, Parr, Ambrose (Andrew 87), Jedinak, Dikgacoi, Scannell (Ramage 90), Murray, Martin (Easter 77).
BIRMINGHAM: Myhill, Carr, Caldwell, Davies, Murphy, Burke, Fahey, N’Daw (Elliott 81), Spector, Redmond (Wood 83), King (Zigic 70).
Referee: Keith Stroud (Hampshire).