That kept them 14 points clear, though other sides have games in hand.
After losing two early wickets, home side Cavaliers made 188 with 54 for Bilal Shafayat, 31 for Nayyar Abbas and 28 for Kashif Ali, Richard Bostock taking 3-35 and Nicholas Keast 3-38.
Cuckney reached 189-8 to win by two wickets with four balls to spare, Nicholas Keast with 50 and Nick Langford with 53, Rehan Ahmed claiming 5-35.
“It was a perfect weekend really,” said assistant captain Bostock.
“ It was nice to get things started off with a win over Cavs.
“It was a very tight game in the end. They probably set us too many runs from the position we had got ourselves in. We thought 160 but they got near 190.
“We were cruising at one point but then maybe made a bit of a meal of the chase and in the end we only knocked it off with one wicket intact due to a freak accident to Oliver Wilson.
“He went over on his shoulder and dislocated it. He was taken to the QMC and eventually made his way back, willing to try to bat but we advised against it. So effectively it was a one wicket victory in the end.”
Against Hosiery Mills, Cuckney made 215-9, Tom Ullyott with 66, James Hawley 33, Nicholas Keast 27 and Tom Keast 24. Daniel Harris took 3-43 and Adam Dobb 3-28.
The 42-run win was then sealed as they bowled out the visitors for 173, despite Patrick Delahunty (65) and Stephen Gooding (37) putting on 81 for the second wicket.
Keshara Jayasinghe added 32 and Bostock took 4-32.
“We went into Sunday knowing that at this stage of the season and with the games in hand we had to take all eight points or the win over Cavs would not have meant a great deal,” said Bostock.
“We went in with full focus and reset from Saturday. We probably scraped taking the full points by about 10 runs but it was really satisfying topped off the weekend.”
This Saturday they host Wollaton and he added: “Wollaton are a decent side with dangerous players, but at home we are very confident of what we need to do.
A busy week sees Cuckney also travel to Kimberley on Thursday in the NPL T20 quarter-finals and at home to Ticknall on Sunday in the Derbyshire Premier Cup second round.