At Newcastle-Under-Lyme side Porthill Park on Sunday, the home team made 243-7 in their 40 overs, Matt Wright taking 3-44, before Kimberley knocked off the winning 244-5 total with an over to spare, Sam Wood with 74, Martin Weightman 69 and Jack Nightingale 50.
“We are now potentially two wins from a final at Lord's which is an amazing thing for the club,” said captain George Bacon.
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“We had amazing support there on Sunday and it was a tight game which we won.
“The competition is something we take very seriously and I am incredibly proud getting as far as we have done. The only time we have reached the last eight before was in 2015 and this time, if we make the last four, the semi-final would be at home.”
After seeing off Notts & Arnold Amateur on Saturday by 175 runs, Kimberley now face one of their biggest rivals, Papplewick & Linby, away this weekend with Kimberley third and Papplwick fourth, two points adrift with a game in hand this weekend.
“There are still a lot of things will need to go our way if we are to climb back to the top of the table,” said Bacon.
“But we are doing all we can and we're on a good run. We are doing our bit in the hope others slip up.
“Cavaliers slipped up last weekend after a very good performance by Hucknall. But we know they're going to have to slip up again, and probably twice, and us win every game to overtake them, so we're not getting too excited.
“Papplewick is a big game and unfortunately we won't be able to put our strongest side out for one reason or another, but it will still be a very strong side.
“What happens in the other games is out of our hands. We are controlling what we can control.”
Last Saturday, winning the toss, Kimberley made 302-7 with Godleman hitting a superb 116, and Martin Weightman 41 with Alex King adding 50 as No.6 batsman.
In reply, Notts & Arnold were bowled out for just 127 in 32.3 overs, Josh Mierkalns with 48 and Alex Burrow with 30, Jack Nightingale taking 3-14 off six overs and King 3-28 off seven.
Bacon had high praise for Godleman, saying: “Billy has been everything we wanted of him since he joined us.
“We had been on the hunt for a second pro for quite a while and he has been brilliant since he came into the club, not just his runs – which have been a huge help – but the way he's been, the help he's given me as captain and the way he's been with all the lads.
“He played very well on Saturday and got us to a total we were confident of defending, which we did very well.”