Green struck with just three minutes to go to give Ian Brightwell's side their second win in 15 games.
Receiving the ball just inside the area he took full advantage of the space afforded to him by a generous Morecambe defence and produced a quality finish to beat Shwan Jalal low to his left much to the visitors' delight.
The goal came as a shock to the home fans as Morecambe had dominated the game for long periods but came up against an in-form keeper in Jonny Brain and wasted a string of golden chances themselves.
Macclesfield, who have enjoyed some excellent away wins this season, started the game well with Danny Thomas forcing a save from Jalal in the first minute of the match.
The Morecambe keeper had to be alert again in the first half to tip over Sean Hessey's free-kick and save low down from Ryan Creswell's close-range effort.
The Silkmen continued to set the early pace with James Ashmore firing over twice in quick succession before a shell-shocked Shrimps found their feet.
Midfielder Stewart Drummond forced Brain into a smart save low to his left from a header after an excellent run and cross from Wayne Curtis and skipper Jim Bentley saw a well-struck shot beaten away by some desperate Macclesfield defending.
Winger Garry Thompson was the Shrimps' biggest threat and should have scored on 20 minutes when found by Curtis free at the far post.
However, he struck his shot into the side-netting when he should have done better. Thompson then headed inches wide after latching on to a moment of hesitation between Brain and left-back Neil Ashton before forcing Brain to make another good save after being put through by Carl Baker.
Morecambe dominated the early stages of the second half but showed a lack of quality in front of goal.
Baker twice curled efforts over after great runs and David Artell headed weakly goalwards from a dangerous Craig Stanley free-kick.
Drummond did find the target but also found Brain in great form with a world-class save low to his left on 57 minutes.
Baker showed his class again in the final minute with a wonderful, mazy run that ended with a low shot that flew inches wide of the right-hand post with Brain beaten.
In the end it was a win that delighted Macclesfield boss Ian Brightwell, who said: "It was a tough game for us.
"We fought it out against a good side and it was a great three points for us.
"We've played well in recent weeks without picking up the result and today we were under the cosh for a while but got the points which were all important.''