Bournemouth's 5-1 win at Fulham on Friday had seen Eddie Howe's men climb to the top of the league - clear of previous leaders Middlesbrough on goal difference.
However, with Derby, Middlesbrough and Watford all failing to win on Saturday, there are now four teams tied on 66 points at the summit.
Jamie Ward put Derby in front against Birmingham with a left-footed strike from close range after Darren Randolph had kept out Johnny Russell in the 20th minute, and Tom Ince doubled the advantage three minutes into the second half.
Steve McClaren's side appeared destined for all three points as the game ticked into stoppage time, but Paul Caddis converted from the spot in the 93rd minute after Ince committed a foul in the box.
Clayton Donaldson then earned Birmingham an unlikely share of the spoils with a dramatic 96th-minute header.
A win would have seen Derby go two points clear at the top, with Middlesbrough losing 2-1 at Nottingham Forest and Watford held to a 2-2 draw at Wolves, where both sides were reduced to 10 men late on.
The top four now have Norwich City breathing down their necks after Alex Neil's side strolled to a 4-1 win at Millwall, piling more pressure on under-fire boss Ian Holloway.
Brentford missed a chance to put daylight between themselves and Ipswich Town as sixth and seventh drew 1-1 at Portman Road.
At the other end of the table, the situation looks increasingly bleak for the bottom three.
In addition to Millwall's thumping at the hands of Norwich, basement club Blackpool lost 1-0 at home to Sheffield Wednesday, and Wigan Athletic were beaten 1-0 by Leeds United.
The waning hopes of those clubs in the relegation zone will be music to the ears of clubs such as Rotherham United, who did their own chances of survival the world of good by climbing up to 20th with a 2-0 win at Huddersfield Town, despite having Lee Frecklington sent off in the second half.
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