Groves once again named himself in midfield, the first team return of Alan Pouton mean a recall for Ash Hildred alongside the player-boss.
Simon Ford continued his recovery from injury in defence, the former Charlton youngster is likely to feature over the Christmas period at some point.
Goals from young County forward David Kettle in each half, both down to poor defending, were enough to beat Town. The Mariners now face a mammoth task of catching league leaders Hartlepool.
Notts County: Deeney, Hannigan, McIntyre, Barras, Bostock, Francis, McFaul, Brough, Riley, Hackworth, Kettle.
Town: Hughes, Hyams, Ford, Wheeler, Young, Bolder, Hockless, Groves, Hildred, Mansaram, Huckett.