Having led at 1-0 and 2-1, Boro shut off in the second half and Nantwich collected all three points.
One change was made by Boro, with Nathan Valentine coming into the starting 11 in midfield, taking the place of Matty Dixon, who missed out through injury.
Boro started well, as Bailey Gooda hooked just over and Nathan Valentine flicked a Michael Coulson set-piece into the Shed.
The hosts got closer and closer, Nantwich defender Toby Mullarkey hitting his own bar with a header that was eventually cleared.
Eventually this weight of pressure told when James Walshaw won his battle in the box and picked out Wayne Brooksby, who rolled neatly into the far corner.
Boro should have been looking to push on from here, but instead they found themselves pegged back soon after.
Some woeful defending from a free-kick let Danny Glover in and he showed how much of a lethal weapon he is from close range by poking home.
Boro swiftly shook off this blow and managed to strike for a second time soon after.
Coulson's quick feet fed Walshaw in the box and the striker, in typical fashion, made no mistake with an angled drive.
Nantwich almost responded within seconds, when Sean Cooke danced through six Boro challenges, but keeper Tommy Taylor tipped his shot away.
The Cheshire outfit continued to fight when the second half got underway, pinning Boro back for a good period of time.
They went close when the ball was given away on the Boro left and Glover guided a cross just over the head of sub Nathan Cotterell.
Having held firm during this worrying period, Boro began to force themselves off the ropes.
They had a couple of useful penalty shouts, with Coulson and Walshaw both going down under challenge in the box, but on both occasions referee David Jones shook his head.
But it was Taylor who was the busier of the stoppers and he was forced to make an amazing stop when Nantwich broke at pace and Glover drilled at goal.
A second Nantwich goal had been coming and it arrived with seven minutes of play remaining. Glover again took advantage of some mediocre defending and he nodded home at the far post.
Things went from bad to worse when Glover escaped unmarked once again and stooped to head home his third and Nantwich's winning goal.