Kidsgrove Athletic manager Ryan Austin made one change to the side which beat Market Drayton Town in midweek with Kingsley Adu Gyamfi replacing James Jennings. The forward dropped to the substitutes bench.
Anthony Malbon had the first chance of the game when he saw his shot deflected over the bar for a corner. From the dead ball, defender James Butler saw his header rattle the crossbar as Kidsgrove looked for their fifth win of the season in all competitions.
Butler's defensive partner, Richard Duffy, was next to go closest when he flicked on a Kyle Diskin free-kick. However, it didn't have enough power to beat Dale Latham in the Glossop goal.
At the other end, Sam Hall had to make a fine tackle to stop Jack Touhy from giving the visitors the lead on 33 minutes.
Butler had two more chances in the first half, which he put over the bar as the former Stoke City youngster looked to get his first goal of the new season.
Glossop left-back Bakari Coulibaly forced a fine save out of Kieran Harrison as he tipped the defender's shot into the side netting to keep it at 0-0 midway through the second half.
Malbon had another chance when he saw his volley deflected over the bar for a corner. From that set-piece, Butler again headed wide of the goal.
With 10 minutes to go, Mablon had a glorious chance to snatch the win, when he was played in one-on-one with the keeper. However, the captain was in acres of space and in the end he put his shot straight at Latham when you would have put your money on the forward to find the back of the net.
The results keep Grove in 13th place in the league table, just three points off Chasetown who sit in 10th place.
Kidsgrove takes a break from league action next Saturday when they visit Matlock Town in the Emirates FA Cup 2nd Qualifying round, we hope to see you there cheering on the Grove.
Kidsgrove Athletic: Harrison, Thompson, Morris, Hall (Rhodes, 88), Duffy, Butler, Diskin (Jennings, 83), Blake, Wiggins-Thomas, Malbon and Adu Gyamfi (Williamson, 60).
Unused subs: Murphy and Savage.
Glossop North End: Latham, Wilshaw, Coulibaly, Touhy, Mwakona, Samass, Ekpolo, Mason, Limpishi (Fitton, 69), Maeico (Czubik, 69) and Mills (Seosolo, 87).
Unused subs: Matthews and Holt.
Attendance: 135