Boro started brightly and on 12 minutes Paul Walker curled a spectacular shot from the edge of the box onto the upright and across the face of goal with the home keeper stranded.
Luke Lofts opened the scoring for the visitors on 17 minutes when he flicked home a low cross from Michael Coulson.
Less than a minute later James Walshaw made it 2-0 to Boro with his third goal in as many games, a quck break allowing Chris Dawson, back from injury, to set the Athletic striker free and he made no mistake.
Midfielder Dawson then let loose with a 25-yard shot midway through the half and his effort flew narrowly wide.
On the half-hour mark Nantwich had their best chance, when from a free-kick, Valdemar Schousboe rose highest and sent a powerful header on target, only for it to be saved brilliantly by Tommy Taylor.
Just before the interval Dawson had to limp off through injury, with Kian Spence taking his place, but Boro maintained their two-goal lead until the interval.
The first 25 minutes of the second half were fairly uneventful, apart from Jack Johnson receiving a caution for protesting to the ref and Walshaw being replaced by Will Annan on 70 minutes.
Six minutes later Josh Langley got a goal back for the home side after a goalmouth scramble, and soon after they levelled the scores through Joe Malkin's neat finish.
Just two minutes later the comeback was complete and Nantwich went 3-2 ahead through a cracking shot from skipper Casper Hughes, and this was enough to secure the win for the Dabbers and leave Boro wondering how they had snatched defeat from the jaws of victory.