Lee Moore put Nuneaton ahead in the 47th minute with Eddie Nisevic adding a second in the 58th minute.
Former Coventry City youngster Ben Mackey scored for Corby Town in a 3-4 defeat to Blyth Spartans.
In the FA Trophy, Leamington had a 3-0 victory against Bamber Bridge. Watched by a crowd of 510, Lewis put the Brakes ahead in the 26th minute before goals from Batchelor (35) and Rowe (38) sent Leamington into the Third Qualifying Round.
Rugby Town are out after going down 3-2 at Stocksbridge Park Steels. Goals from Keen and Preston pulled it back to 2-2 but Ring hit the winner in the third minute of stoppage time.
In the Southern League Central Division, Bedworth United lost 2-0 at AFC Hayes.
Stratford Town went down to a 6-1 defeat at Coalville in the Midland Alliance.
Curtis Jackson hit a hat-trick for Covenry Copsewood in a 4-0 win over Pilkington. Alveston lost 2-1 at Bolehall Swifts.
In Midland Combination Division Two, Leamington Hibs beat Perrywood 3-0 but Young Warriors lost 2-1 at home to Henly Forest.
In Division Three, Coventry Amateurs beat JDG Alliance 2-1.
It was Coventry Telegraph Cup day and Racing Club Warwick beat Triumph Athletic 2-1, Southam United beat Christ The King 2-0, Kenilworth Town beat Massey Ferguson 3-0 whilst Nuneaton Griff won 4-0 at Woodlands.