
The Seasiders trailed midway through the second half at the Optimum Pay Stadium as Joel Stair's header opened the scoring for the hosts.
Whitby, who were in good spirits following a 2-0 win over Bamber Bridge the previous week, were unable to find an equaliser in a well below par performance.
Lee Bullock and Nathan Haslam named an unchanged starting eleven from the one that won at home the previous week, whilst new loan signing William Lancaster was on the substitutes' bench.
The two sides had already met twice in the 2021/22 season with Whitby claiming a 2-0 victory in the reverse league fixture. The other match came in the Buildbase FA Trophy as the Blues suffered a disappointing 1-0 home loss against the Dabbers, who would go on to lose at Kings Lynn Town in the next round.
Nantwich goalkeeper Matt Gould produced an important save to deny Bradley Fewster, blocking the former Middlesbrough man's close-range effort in the first two minutes.
Gould then saved well with his feet to keep Josh MacDonald out ten minutes later before Nantwich started to grow into the game with Dan Cockerline firing over the bar from a tight angle.
Fewster called Gould into action for a second time in the 33rd minute, with the host's shot-stopper being able to hold his effort, before Whitby were fortunate not to fall behind just before the break when Shane Bland acrobatically saved from Jamie Morgan.
In the second-half, Jacob Bickerstaff fired wide of Bland's post with a powerful strike, before the Blues' keeper then saved well low down to his left following a Nantwich corner.
With Nantwich starting to show some form of control in the game, the Seasiders were dealt a devastating blow as Stair netted in the 63rd minute.
After a corner was played in towards the near post, the Nantwich captain rose highest to head into the ground and eventually beyond Bland.