The first half was dull but dominated by Chelsea, who failed to muster any shot of note on goal.
That all changed in the second period as Freda Ayisi sent Birmingham ahead, only for Eni Aluko to level matters.
However, neither side could grab the all-important third goal in the game, and were made to settle for a point.
Both teams were in cup action last weekend, although enjoyed contrasting fortunes. Emma Hayes' Chelsea fell to a dramatic defeat to London Bees on penalties. A rotated side on the day had a more normal look to it on Sunday. Fran Kitching, Hannah Blundell, Niamh Fahey, Eni Aluko, Bethany England and Alessia Russo all dropped out for Hedvig Lindahl, Millie Bright, Ana Borges, Katie Chapman, Claire Rafferty and Ji So-Yun.
David Parker's side claimed a 2-0 over Oxford United Ladies to make it through to the next round of the Conti Cup last time out. He made just two changes from that side, replacing Isabelle Linden and Sophie Baggaley with Charlie Wellings and Ann-Katrin Berger.
First half fails to excite
The opening exchanges between second and third in the league was always going to be close, yet neither side were able to muster a shot on target in the opening 20 minutes. Gemma Davison's strong run and shot was bravely blocked by the Birmingham back-line, while the visitors continued to threaten from set-pieces.
Emily Westwood was in the thick of things at either end and a nasty bump to the head saw the defender require lengthy treatment. Unfortunately for Parker, she was unable to continue and Chloe Peplow was brought on. It was her partner, Jess Carter, that made a crucial intervention to deny Davison from darting through on goal once more.
As the half drew on, Birmingham's attacking threat began to fade and Chelsea come forward with increasing regularity. Berger was tested for the first time with a tame header from Gilly Flaherty, while both Davison and Chapman went close on separate occasions with hopeful efforts.
The attacking talents of Davison were clear to see, but Karen Carney was running the show against her former club in some style. Her spins and touches were starting to open up some space in the middle, and Davison finally gave Berger something meaningful to do; her shot was, however, well held by the German before the half-time whistle.
Stunning start to the second half
The first half had been all Chelsea, but Birmingham struck at the beginning of the second half to shock the champions. A poor pass across goal was touched through the legs of Bright by Wellings. The clever touch allowed the attacker time on the ball to pick out her partner, Ayisi. The visitors' top scorer wasn't going to pass up their golden chance, rifling across goal with her right foot to find the bottom corner; Lindahl was powerless to prevent it from finding the bottom corner.
But that was seemingly just what Chelsea needed, and they sprung into life. Aluko was brought on for Drew Spence and had the impact Hayes wanted, scoring less than five minutes after coming on. Ji's pass from midfield was inch-perfect to find the England international, who drove to goal and slotted a wonderful finish past the oncoming Berger.
Chelsea turn on the style but can't find a winner
The turgid first-half was soon forgotten about and the hosts' attacking verve had returned. Carney and Aluko exchanged passes before a snappy one-two resulted in the latter firing a shot just past the post. Chapman had another effort from outside the area on the hour mark, though it also flew wide.
Davison had been quiet in the second half, in comparison to the first, but suddenly sparked with a magnificent solo run. She rounded and rocked past defenders with ease before firing across the face of goal, only to see no-one at the other end to finish the move off.
Despite the best efforts of Chelsea's attacking and Ayisi for Birmingham, neither side could grab a late second goal. Chapman was sent off late on for a debatable second yellow card after she tangled with Ayisi, in what was the only real talking point in the final few minutes. Both sides will play again next Sunday, with Chelsea taking on Arsenal and Birmingham facing Sunderland. The hosts remained in second, now a point behind City; Birmingham moved above Liverpool into fourth.