Alex McLeish's side climbed above West Ham on goal difference into 17th spot as they battle to beat the drop.
The Blues had got off to a dream start when Chilean winger Jean Beausejour fired them into the lead on 17 minutes with a powerful header for his second goal in as many games.
However Dutch midfielder John Heitinga struck for Everton just before half-time, lashing in a firm shot that flew past Birmingham keeper Ben Foster after the Blues failed to deal with a corner.
Birmingham barely created anything thereafter although despite enjoying a wealth of possession, Everton were unable to make their dominance count.
Everton striker Louis Saha was denied by a diving block from Blues midfielder Jordon Mutch while Jermaine Beckford also tested Foster with a close-range shot that was well saved by the Birmingham keeper.
Birmingham out of drop zone as Everton held
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