The Yeltz had taken the lead through Ashley Sammons with a 30-yard wonder strike only to be pegged back after Reece Hewitt was sent off,
However, sub Gibson struck with just four minutes left to go firing underneath the keeper to secure the victory in the Southern Central Division One clash.
In the National North, Kidderminster Harriers were well beaten by Brackley Town at Aggborough.
Correy Davidson got Harriers’ goal just before half-time – but they were already 2-0 down at that point.
A third goal for the visitors in the second half completed a 3-1 defeat.
Stafford Rangers collected a point with a goalless draw at home to Basford United in their Northern Premier League clash.
Rangers had a goalbound header cleared off the line in the second half in the closest effort to a goal in the encounter at Marston Road.
Sporting Khalsa v Belper Town (FA Cup preliminary qualifying round replay - winners at home to Southern Central Premier side Alvechurch on Saturday in first qualifying round).
n Hednesford Town and Rushall Olympic will face Football League opposition in the first round of the Birmingham Senior Cup next month.
Full draw (ties to be played on or before October 26): Nuneaton Borough v Coventry Sphinx, Bedworth United v Romulus, Banbury United v Racing Club Warwick, Stratford Town v Wolverhampton Wanderers, Halesowen Town v Coventry United, Coleshill Town v RAF Representative, Solihull Moors v Boldmere St Michaels, Hednesford Town v Burton Albion, Rushall Olympic v Walsall, Stourbridge v Lye Town, Rugby Town v Coventry City, Alvechurch v AFC Wulfrunians, Leamington v Highgate United, Tamworth v Birmingham City, Redditch United v West Bromwich Albion, Sutton Coldfield Town v Tividale.