Ross County's promotion drive was halted by an Alex Williams first-half goal which earned Clyde a victory.
The game came to life in injury time when Clyde's Williams and David Cowan were yellow carded after a jostling match on the touchline.
Just 30 seconds later County's Stuart Taylor was sent off for a foul on Eddie Malone.
Clyde substitute Romauld Bouadji headed off the line in a goalmouth scramble to ensure his side's win.
Clyde: Jarvie, Higgins, McKeown, Malone, Masterton, Bryson (Dick 81), O'Donnell, Harris (Bouadji 65), McGowan, Williams, Thomas Brighton (Hunter 87). Subs Not Used: Bradley, Cherrie.
Goals: Williams 25.
Ross County: McAldon (Garden 13), Cowan, Lauchlan, Canning, Djebl Zadi, Rankin, Tiernan (Webb 58), McCulloch, Burke, McSwegan (Taylor 70), Winters. Subs Not Used: Cowie, McGarry.
Sent Off: Taylor (90).
Ref: S Dougal