Birmingham City came from two goals down to extend their unbeaten run in the npower Championship to six matches.
Bristol City went ahead in the 21st minute through Stephen Pearson's superb strike and, in a first half of few chances, surged into a two-goal lead thanks to Jon Stead's effort.
Birmingham, who took most of the first half to settle, pulled a goal back thanks to King's deflected effort just before half-time and levelled on the hour mark courtesy of Zigic.
The home side pushed hard for a winner in the last third of the game, but in the end Chris Hughton's men had to make do with a point.
Zigic and Andros Townsend returned to the Birmingham starting line-up in place of Guirane N'Daw and Wade Elliott, while Colin Doyle began in goal for the Blues after regular keeper Boaz Myhill was injured in the warm-up.
Bristol City manager Derek McInnes made three changes to the side that beat Coventry 3-1 last time out.
Chris Wood came into the Robins' XI up front, with Brett Pitman suspended, while Louis Carey replaced Ryan McGivern in defence and Martyn Woolford and Kalifa Cisse were handed starts in midfield.
After a slow opening to the match, Birmingham came close to edging in front in the 12th minute.