Aitor Karanka's side are battling with Burnley and Brighton for the Championship's two automatic promotion places and their attempt to secure one of those lucrative berths in the top-flight was dented at St Andrews.
Middlesbrough's point took them to the top of the second tier table with a one point lead over second placed Burnley and third placed Brighton.
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But they were still left fuming after Daniel Ayala's goal, which would have proved the winner, was wrongly ruled out.
Ayala netted in the second half with a fine finish, only to see his effort disallowed for offside even though the former Liverpool centre-back was clearly onside.
"Normally in football when you score one more goal than the opponent you win the game. It didn't happen because Daniel's goal was disallowed and I can't understand why," said a furious Karanka.
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"I prefer to think it's a mistake, but what makes me concerned is a few mistakes have come against us. I feel we have played in different conditions than other teams."
Stephen Gleeson had put Birmingham ahead in the 33rd minute with a powerful strike from 25 yards.
Jordan Rhodes bundled home Middlesbrough's equaliser five minutes before half-time when Birmingham goalkeeper Adam Legzdins spilled a Gaston Ramirez shot.
Ramirez edged Middlesbrough in front in the 57th minute with a close-range header, but Davis equalised 11 minutes later with a superb half volley from the edge of the penalty area.
Burnley, who host QPR, and Brighton, who have a home fixture against Derby, would both move two points ahead of Middlesbrough if they win their matches on Monday.
But Middlesbrough's promotion fate is still in their own hands as they host Brighton in a titanic final day showdown when a win would end their seven-year exile from the Premier League.
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