The home side were reduced to 10 men in the second half when Josh Brooking took down Dillon Hoogewerf just outside the area, but it was the Blues who found the lead soon after, Harvey Vale tucking home from the penalty spot.
Alvaro Fernandez, who had dominated much of the game from left-back, brought United back level in the 87th minute, rifling a left-footed strike past Teddy Sharman-Lowe.
FIRST HALF
United sprang out of the blocks at the Bridge, a string of nearly-chances coming within the first couple of minutes. Shola Shoretire showed nice footwork on the edge of the box before sending a teasing ball into the area which was cleared for a corner.