Watched by a crowd of 252, James Armson opened the scoring for Kevin Wilkin's side in the 45th minute. Tom James levelled in the 50th minute only for James Marsden hit the winner for Nuneaton three minutes later.
Chasetown are also through after winning 2-1 at last year's finalists Alvechurch.
A crowd of 165 was at Sheepy Road to see Atherstone drew 1-1 with Rugby Town in a Southern League Central Division game. Preston scored for VS in the 83rd minute but the Adders equalised through Wood in the 87th minute.
In the same division, Bedworth United lost 2-1 at home to Daventry Town. Berwick scored for the visitors in the 40th minute and then converted a penalty three minutes into the second half. Levi Ramsey pulled one back in the 69th minute but the majority of the 140 crowd went home unhappy.