Adam Stevens named the same side that beat Lancaster last Saturday.
The Gingerbreads had the ball in the back of the net in the opening minutes, but Stefan Galinski was ruled offside.
The first half saw plenty of chances for The Gingerbreads, as they attacked down the slope however they could not find a way through. Kidsgrove had chances to take the lead, but the The Gingerbreads defence stood firm.
As like last week, The Gingerbreads stepped up a gear in the second half. However with chances coming and going it looked as if a replay was going to happen.
With 8 minutes to go and The Gingerbreads fighting to get a goal, up stepped an unlikely scorer. Curtis Burrows beat two Kidsgrove defenders and play in Stefan Galinski who buried his shot passed the goal keeper, to send the travelling supporters wild.
Kidsgrove were not settling for defeat and pushed on, The Gingerbreads defence again stood resolute.
With 4 minutes of injury time added, it was Lee Shaw who was able to wrap up the win at the very end. He broke free into the box and was toppled by the Kidsgrove defender, the referee had no choice and pointed to the penalty spot. Shaw stepped up to take it himself and fired the ball home.
The draw for the next round is Monday lunch time with sides from the National League North and South join the competition.