Marsden put Nuneaton ahead in the 11th minute, Nisevic added a second three minutes later and in the 19th minute, Moore scored a third for Kevin Wilkin's side who neither scored or conceded for the rest of the match.
In the Southern League Premier Division, Lemaington went down to a 1-0 defeat at Tiverton Town. Faux scored the goal in the 53rd minute.
Atherstone Town lost 2-1 at home to Slough Town. Smith scored for the Adders in the 38th minute but the visitors levelled in first half stoppage time through Slipetts and Seeby hit the winner in the 75th minute.
Bedworth United lost 1-0 at home to Hitchin Town. Howell scored the only goal of the game in the 45th minute.
Rugby Town did manage a victory, beating North Greenford United with goals from Wesley and Alexander.
In the Midland Alliance, Stratford Town won 6-0 at manager-less Willenhall Town.
In the FA Vase, Coventry Sphinx beat Brocton 1-0, Southam United were held 1-1 by Thurnby Nirvana after extra time, Coventry Copsewood drew 3-3 at Dudley Town.
In the Midland Combination Premier Division, Alveston won 3-1 at Massey Ferguson, Nuneaton Griff drew 1-1 at Dostill Colts but Racing Club Warwick lost 6-2 at Cadbury Athletic.
In Division One, Kenilworth Town drew 3-3 at Northfield Town whilst in Division Two, Leamington Hibernian lost 2-1 at Greenhill.
Coventry Amateurs lost 4-2 at home to Dosthill Colts Reserves but Stratford Town A beat J.D.G. Alliance 12-2.