West Brom travelled to St Andrews knowing a win would see them go third in the table ahead of Saturday's fixtures.
But they were on the back foot for long periods against Garry Monk's men, who took the lead in the 26th minute when Jota capitalised on poor marking to flick home from a tight angle after Lukas Jutkiewicz's header down to the far post.
The winger was then presented with a golden chance to make it 2-0 three minutes later after Kyle Bartley inexplicably handled a right-wing cross. However, Sam Johnstone kept out the Spaniard's low penalty, and the Blues were left to rue the miss.
As with the opener, the defending was suspect when Matt Phillips fired a 39th-minute leveller beyond Lee Camp, while there was a distinct lack of quality at the other end for Birmingham four minutes later when Che Adams blazed over from close range.
It was Birmingham who had the better of the second half yet they could not find a way to beat Johnstone - and the Baggies almost snatched the points when Harvey Barnes rattled the crossbar late on.
Birmingham's wait for a first win of the league campaign goes on, this draw marking their fifth from seven matches, while West Brom sit in fifth, three points off the automatic promotion places.