The home side rescued a point but were indebted to substitute Eni Aluko, who stepped off the bench to replace Drew Spence and soon after raced on to Ji So Yun's through ball to side-foot home a 53rd-minute equaliser
Freda Ayisi had given Birmingham a 48th-minute lead with a clinical finish from the visitors' first shot on target.
England midfielder Chapman was given her marching orders in the 86th minute following her second yellow card for a foul on Ayisi.
Arsenal leapfrogged Birmingham and Liverpool into third place in the table following a 2-0 home win against Notts County as Jordan Nobbs turned in a player-of-the-match display by scoring one and setting up another
England midfielder Nobbs' searching long ball set up Danielle Donk, who coolly converted to put Arsenal ahead in the 10th minute.
Arsenal extended their lead in the 55th minute when Nobbs got on the end of a neat passing move to fire home with the Londoners securing fourth league win of the season.
Source : PA
Source: PA