Craig Westcarr whipped in a cross from the right, the ball skimming up off the surface to Davies in the six-yard area and he diverted the ball past on-loan Manchester United goalkeeper Tom Heaton.
Rochdale levelled within five minutes after Chris Dagnall was felled by Jamie Clapham as he shaped to shoot. Referee Nigel Miller awarded the penalty and Dagnall converted from the spot.
Sven Goran Eriksson, among the crowd at Spotland, would not have been impressed with County's defending when the hosts took the lead in first-half injury time.
A long punt up field by Nathan Stanton should have been cut out by either Lee or Stephen Hunt - instead the pair collided, sending each other crashing to the turf and leaving the path to goal clear for Chris O'Grady. He rounded Kasper Schmeichel and slid the ball into the empty net.