Elgin completed a late fightback to draw 3-3 and deny Clyde a rare win in Jim Duffy's first game as manager.
The home side took the lead after just four minutes through John Stewart but City levelled as Jason Crooks scored from the penalty spot midway through the first half.
Clyde then retook the lead with a penalty of their own from Marc McCusker before Elgin's David Gormley missed from the spot in the second-half.
A minute later Nicki Paterson capitalised to put Duffy's side 3-1 ahead with 20 minutes to go.
But two late headers from Gormley and Craig Frizzel denied the home side a vital victory as Clyde finished the game with ten men following McCusker's dismissal for a second bookable offence.
The Bully Wee remain bottom of the Scottish Third Division, thirteen points adrift of East Stirling in ninth.