Sean Cooke's early free-kick, placed in to the empty corner of the goal as Yellows 'keeper Charlie Albinson lined up his wall, and Joe Mwasile had The Dabbers 2-0 in front at the break.
In the proverbial game of two halves, Warrington threw everything at the hosts in the second half and should have got at least a goal back before Adam Hughes' free kick gave them hope 16 minutes from time.
Dominic Reid had a goal ruled out for offside at the death as Nantwich held on to make it six wins and three draws in their nine home games so far.
It was the only league game of the night with other clubs engaged in FA Trophy and Integro League Cup action.
The Dabbers are second in the EVO-STIK League Premier Division table, five points behind leaders Scarborough but with a game in hand.
Previous leaders Warrington have now lost their last two league games, but still have the best points per game average in the league.
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