David Mooney broke the deadlock after 23 minutes, finding the top corner with a well-placed right-foot shot from 15 yards after City’s back-pedalling defence had failed to deal with a quick break.
But Bristol City refused to buckle and deservedly equalised in the 58th minute when Aden Flint nodded down a right-wing corner from Scott Wagstaff and Baldock spun to shoot home from close range.
Dean Cox restored Orient’s lead in the 69th minute with a simple tap-in after City goalkeeper Elliot Parish had failed to hold a shot straight at him from Moses Odubajo.
But two minutes later former West Ham striker Baldock beat two defenders to cut in from the right and saw his low cross-shot deflect in off Orient defender Scott Cuthbert.
Both sides had chances to win in a thrilling second half and a point apiece was about right.