The striker latched on to a loose ball in the box in the 68th minute, before turning Krystian Pearce and volleying past Kevin Pilkington.
It meant that in six Meadow Lane matches between the sides since their first
Magpies boss Ian McParland was forced into one change to his starting eleven from that which began the 3-0 FA Cup first round victory over Histon last week, as playmaker Neil MacKenzie missed out with a hernia injury.
Matt Somner replaced him in midfield, while Town boss Ian Brightwell chose to shake thing up following their Cup exit to Rushden and Diamonds with three changes as Sean Hessey, Jamie Tolley and Green earned recalls.
The Silkmen began the match with a defensive 4-5-1 formation, and immediately began to infuriate the majority in the 4,390 attendance with time wasting tactics.
Indeed, it seemed clear Brightwell's team would be happy with a point with County going into the encounter having won three of their last four.
It was the hosts who threatened first with Lawrie Dudfield firing over in the first minute after a good run by Richard Butcher.
Town's leading scorer Martin Gritton hobbled off after just six minutes after a strong but fair challenge from stand-in County captain Adam Tann, with Gritton replaced by Gareth Evans.
County's early pressure nearly told with seven minutes on the clock as Butcher again worked his way inside to meet a Paul Mayo cross, but after turning past Kevin McIntyre, Butcher could only fire at Lee from six yards out.
The visitors were showing little in the way of an attacking threat, with the game developing into a midfield battle but Tolley did have a shot on goal for Town after 25 minutes, hitting straight at Pilkington.
At half-time both managers made changes, Brightwell introducing Jimmy McNulty for Hessey, and McParland replacing Andy Parkinson with Myles Weston.
On 50 minutes, Weston's burst down the wing and deep cross fell to Butcher, but he could only steer his effort into the side netting.
Three minutes later Murray collected a McIntyre throw but lashed wildly over from the edge of the box.
Dudfield looked to have given County the lead on 54, after good play by Lee Canoville found him in space inside the box, and his powerful drive seemed to be going in before Lee's outstretched hand brilliantly turned it over.
Tann was then forced into a fine last ditch challenge to deny a roaming Green, before at the other end the County man headed a Mayo cross over.
Then came Green's 62nd minute goal, somewhat against the run of play as he smashed past Pilkington on the volley in front of the small section of visiting fans, for his sixth of the season.
It seemed to breath new life into Town who then had chances through Evans and Thomas but both missed the target.
Spencer Weir-Daley and Hector Sam were introduced for Somner and Craig Lindfield for County, but it was Tann who again threatened when his free header was cleared off the line by McNulty after 75 minutes.
As the game neared it's climax Weir-Daley had one last late chance, after Canoville's centre found him unmarked in the box but he steered his volley agonizingly wide and Town again prevented a County Meadow Lane win.