The Robins though will be happier with the result than their hosts, who are still nine points adrift of the leaders and needed a victory to put pressure on the top two sides.
Charlton dominated the first half but Bristol City took the initiative once they had levelled the scores and will consider themselves unfortunate not to have got all three points.
The West Country side have been the shock team in the Championship this season and are on course to return to the top-flight of English football for the first time in 28 years.
But it was Charlton who took the early initiative after just eight minutes when a flowing five-man move ended up with Darren Ambrose scoring his ninth goal of the season.
Jerome Thomas had a couple of efforts which went close for Charlton, while Dele Adebola - whose head was swathed in bandages after stitches in a head wound - went close with a header.
Bristol City took control in the second half with Michael McIndoe firing over the bar and then having a shot saved and it was no surprise when they equalised with Jamie McCombe heading home from a Lee Johnson's corner.
In a flurry of goalmouth action, Charlton's China International Zhi Zheng twice had close-range shots saved and blocked, but the Addicks had two lucky escapes in the final stages of the game.
First McIndoe hit the post from a curling free kick from just outside the penalty area and then substitute David Noble, who had only been on the field a couple of minutes, saw his close-range effort desperately scrambled away for a corner by the home defence who were hanging on at the end.