The Addicks fought back from two goals down to earn a point in a tightly contested affair at St. Andrews.
Both sides headed into Sunday's proceedings level on points with an eye on edging their way up the Barclays Women's Championship table.
It was an evenly poised opening ten minutes with neither side posing a real threat on goal. Jade Pennock's effort in the seventh minute deflected off Ashley Hodosn but in the end, it was a comfortable gather for Sian Rogers.
Birmingham had a big chance in the 20th minute when Christie Murray's free-kick fell to Gemma Lawley but she blazed her shot over the bar.
Soon after Freda Ayisi looked to catch Lucy Thomas off her line the midfielder attempted a chip which just scraped over the bar.
Darren Carter's side found their breakthrough in the 34th minute when Jade Pennock scored from close range following a scramble in the box from a corner kick.
Charlton then found themselves two down five minutes after the interval after Christie Murray's corner ball lofted over to the back post for Louise Quinn to head it home.
The Addicks responded almost immediately after a short corner ball found Beth Roe, her strike deflected off Kiera Skeels' shin and into the roof of the net.
Hills then made some attacking changes to her side bringing on Emily Simpkins, Corinne Henson and Lois Roche.
Charlton found an equaliser ten minutes from time when Lois Roche broke through in the middle of the park, she shifted the ball over to her left and then Melissa Johnson buried hwe shot into the bottom corner beyond Thomas' reach.
Charlton piled on the pressure in the final exchanges with Simpkins coming close, but in the end, the points were shared at St. Andrew's.
Charlton: Rogers, N'Dow, Johnson, Follis (Hennessy 78), Ayisi, Bruton (Simpkins 65), Addison, Skeels, O'Rourke (Logan 78), Roe (Henson 65), Ross (Roche 73)
Substitutes (not used): Gray, Soper
Booked: Bruton
Goals: Skeels, Johnson
Birmingham: Thomas, Quinn, Pennock, Murray, Hodson, Wilson, Lawley, Devlin, McLoughlin, Jenner
Substitutes: Jones, Simkin, Bourne, Quinn, Estcourt, Walker, Worsey, Banaras
Booked: Lawley
Goals: Pennock, Murray
Charlton return to The Oakwood on Sunday, March 26th to take on Sunderland, click here to secure your tickets
