Brian Gilmour gave Clyde the lead in the 47th minute, when he curled the ball high into the net from 15 yards.
But Sean Higgins scrambled the ball home from close range two minutes later after Clyde failed to clear a corner.
Michael McGowan scored from the spot after Dougie Imrie was fouled by Mark McCulloch, but Adams pounced after David Hutton parried a shot clear.
Ross County: Tomie, McCulloch, Moore (Gunn 76), Dowie, Keddie, Adams, Scott, Higgins (O'Carroll 69), Shields, Cowie, Robertson. Subs Not Used: Samson, Webb, Gardyne.
Booked: Keddie, Adams, Moore.
Goals: Higgins 49, Adams 79.
Clyde: Hutton, Harris, McCann (Bradley 72), Higgins, McKeown, Masterton, Bryson, Gilmour, Arbuckle (Williams 86), Imrie, McGowan.
Subs Not Used: Cherrie, Hunter, Ferguson.
Booked: McKeown, McGowan.
Goals: Gilmour 47, McGowan 63 pen.
Att: 2,145
Ref: C Allan
