Kyle Storer put Nuneaton ahead in the 49th minute but two minutes from time, McGivern equalised.
Leamington were beaten 3-2 at home in a Southern League Premier Division fixture. Husband and Corbett scored for The Brakes after they had gone 3-0 down against Cambridge City.
In the Central Division, Rugby Town thrashed Soham Town Rangers 5-1. Keen hit a hat-trick with other goals coming from Connelly and Hamilton.
Atherstone lost 3-1 at home to Hitchin Town with the visitors goals coming after Smith had given The Adders a tenth minute lead.
Bedworth United's home game against Northwood Town was postponed.
In the Midland Alliance, Stratford beat Bridgnorth 3-0.
Massey Ferguson's and Coventry Copsewood's Les James Cup were postponed.
Alveston beat Bolehall 2-1 with goals from Wilkes and Ward, Southam drew 1-1 at Pilkington whilst Nuneaton Griff lost 4-1 at Bartley Green.
In Division One, Kenilworth Town drew 3-3 at Coton Green, whilst in the Challenge Vase, Young Warriors lost 4-2 at home to Continental Star Reserves.
Stratford Town A won their Division 3 game at Dosthill Colt Reserves but Future Legends lost 7-1 at Polesworth.