The Pirates looked to be heading for defeat in League Two on Boxing Day after a Craig Reid penalty put Aldershot in front with 14 minutes to go but Richards, who had only come on five minutes earlier, salvaged a point at the Recreation Ground.
Michael Hector gave the Shots a half-time lead with an exquisite first-half strike but a 54th-minute penalty from David Clarkson drew the Pirates level.
Hector slotted the ball into top corner after a lay-off from Danny Hylton's gifted him a yard of space on the edge of the area.
Six minutes into the second half Aaron Morris brought down Tom Eaves in the area in Bristol's first meaningful attack of the game, Clarkson duly held his nerve, despite the torrential rain, to fire home.
Reid restored the lead with coolly-taken penalty of his own but a scuffed effort from Richards in the 87th minute slowly trickled into the net after scrappy Aldershot defending to give Ward some comfort in his first game back.