The match had looked to be heading for a draw until the striker curled a superb effort into the top corner in the third minute of injury time.
The home side had taken the lead early in the second half through Asamoah, but were pegged back by substitute Kevin Townson's header 15 minutes from time.
Chester had started the game brightly and on nine minutes Asamoah saw an effort parried away by keeper Tommy Lee.
Three minutes later the visitors threatened as Danny Whitaker played a dangerous ball across the face of goal that just evaded Andrew Teague's efforts to reach it.
The difficult conditions made free flowing football difficult as both sides struggled to come to terms with the swirling wind.
On 18 minutes Asamoah had his back to goal and turned smartly to hit a left-foot shot just a foot past the post from ten yards.
Jake Edwards then had a half chance and Ben Davies rifled a 20-yard effort narrowly wide as Chester, using the wind blowing in their favour, put pressure on the Silkmen.
Five minutes before the interval Edwards hit a left-footed effort just past the post and then a glancing header from Stewart Drummond just drifted past the same post.
The home side got the breakthrough their pressure deserved five minutes after the restart when a left wing cross from Sean Hessey found Gregg Blundell at the far post and he headed the ball into the path of Asamoah who volleyed home from close range.
On the hour mark Chester were unfortunate not to double their advantage when a corner taken by Davies was swung in and came back off the post.
Macclesfield substitute Townson shot wildly over with a half chance, but made no mistake on 75 minutes when he beat the Chester keeper Chris MacKenzie to the ball to head it into the net for the equalizer.
A late 25-yard effort from Hessey came within inches of finding the back of the net, before Asamoah's late, late strike stole the points.