It was also the third successive season that the league fixture at the Novus Stadium has finished in a draw.
Neil Baker made one change to the side that drew with Alvechurch with Stoke City loanee Scott Wara starting in defence in place of Joe Kearns.
Grove made most of the running early on and took the lead on 13 minutes when Lee Cropper crossed low across goal from the right leaving Ant Malbon the simple task of tapping in from close range.
The home side went close again with a Jon Beaumont header from a corner before Niall Maguire was replaced by Sam Grimshaw in the 25th minute.
Blues came close in the 33rd minute when Dan Trickett-Smith fired in a free-kick which Kidsgrove goalkeeper Dave Parton did well to push around the post.
Straight after half-time Malbon found himself through on goal but Danny Roberts made the block and saved the follow-up from Cropper.
Leek then had two great chances from right wing crosses. Rob Stevenson whipped the ball in but Grimshaw headed over from close range.
Moments later it was Trickett-Smith who crossed for Tim Grice, who headed against the crossbar.
Roberts made a stunning save on the hour to keep his side in the game. Malbon set up Cropper who looked certain to score until Roberts at full length fingertipped his effort wide of the post.
Trickett-Smith fired a free-kick just over on 70 minutes, but five minutes later he made no mistake.
A foul centrally on the edge of the box saw Trickett-Smith smash home the free-kick into the top corner giving Parton no chance.
Leek finished the stronger and a mazy run by Trickett-Smith in the 79th minute ended with his angled shot saved by Parton.
It was Parton to the rescue again in the 88th minute when substitute Jordan Johnson saw his fierce effort parried away to safety.
Both sides had their chances and both goalkeepers played a big part in keeping the scores level which on the balance of play was just about right.
View the match photos here.
Team: Roberts, Lemon (Davies, 67), Green, Grocott (Johnson, 75), Wara, Chadwick, Maguire (Grimshaw, 25), Hall, Grice, Trickett-Smith, Stevenson
Unused subs: Whitehead, Kearns
Yellow card: Johnson
Updated 09:18 - 17 Feb 2018 by Stevie R