David Turnbull and Leigh Griffiths got the goals, with a greater cutting edge in the second half the hoops could have hit five or six but at the other end of the park a clean sheet was a tentative step forward.
Three weeks ago County recorded a 2-0 win in the Betfred up but there was never any prospect of a repeat with John Hughes replacing Stuart Kettlewell in the dug-out following Saturday’s home defeat from Hamilton Accies.
Celtic’s lack of width was highlighted by their opening goal. In the 24th minute Jeremie Frimpong caused panic in the visitors defence when he hit the by-line with Turnbull perfectly placed to sweep the ball into the net from six yards out. That sort of move was rarely repeated.
Griffiths missed two decent chances early in the first half but made no mistake just past the hour mark when he placed a header from a Ryan Christie ross beyond Ross Laindlaw.