Leek boss Neil Baker made two changes to the side that were beaten by Trafford on Saturday with Marc Grocott and Aaron Bott replaced by Niall Maguire and Tim Grice.
Blues made a nervy start with Kidsgrove having the bulk of the possession in the early stages and the visitors almost went in front on 10 minutes when a speculative long-range effort by Anthony Malbon had Danny Roberts scrambling to push the ball over the crossbar.
It took 20 minutes for Leek to mount a serious attack when Rob Stevenson whipped in a great ball from the right that neither Dan Trickett-Smith or Tim Grice could quite get their heads to.
Roberts saved Leek on 29 minutes when he got down well to make a tremendous block from a close range effort by Chris Budrys. He was called on again a minute later, holding a low effort by his near post.
Grice then had a chance when a ball bounced through but his attempted lob didn’t have enough on it and was gathered by Kieran Harrison in the Grove goal.
Stevenson went on a great run in the 35th minute beating three defenders to cut into the box, but his shot was half-blocked by a defender which took the sting out of it and Harrison saved.
The game had become more even now and continued that way after the break until the 55th minute when Grove went in front.
A good interchange of passes involving Malbon found Budrys near the penalty spot and he swept the ball beyond Roberts into the far corner of the net.
Grice connected well with a header on the hour but Harrison was equal to it to push the ball over the crossbar.
Blues had a lucky escape four minutes later when a goalmouth scramble saw an effort saved by Roberts and the ball hacked off the line.
Town equalised in the 67th minute when Lewis Short fired a deep free-kick into the box, the ball was headed on goalwards by Darren Chadwick and Grice bundled the ball home from about two yards out.
At this stage it looked like Leek had the impetus to go on and win the game, but they were stopped in their tracks ten minutes later when Grove went back in front.
The ball was worked out to Rhys Thompson out on the right wing and his attempted drilled cross flew across goal, hitting the far post and going in.
Baker threw on Jordan Johnson and Aaron Bott in the closing stages, but it was to no avail and Leek suffered a second successive home defeat.
1. Danny Roberts
2. Niall Green
3. Lewis Short
4. Niall Maguire (17. Jordan Johnson, 81)
5. Darren Chadwick
6. Jack Sanders
7. Charlie Walford
8. Billy Reeves
9. Tim Grice
10. Dan Trickett-Smith (12, Aaron Bott, 87)
11. Rob Stevenson
Unused subs: 14. Marc Grocott, 15. Lee Wilsahw, 16. Scott Lycett
Yellow card: Niall Maguire
Updated 21:20 - 18 Mar 2019 by Stevie R