Cuckney are one point off second place and eight off top spot in a tight battle for the Notts Premier League title.
They despatched Hucknall with relative ease at Langwith Road, piling up 221 for nine before bowling out Hucknall for 159.
Cuckney, asked to bat, recovered from losing an early wicket as 54 was added by Tom Keast (36) and Will Butler (45).
After that, though, several batsmen made starts, but none could get beyond 21 until Elliott Bowles landed lusty blows in his 45 not out, including four sixes and a four.
The number 10 batsman then claimed three early wickets as Hucknall were reduced to 26 for five.
None of their top five made it to double figures before, from 93 for eight, Harry Finch (66) temporarily held up the home victory charge.
Jack Cattrall also took three wickets for Cuckney and Jake Tong two as the win was achieved in the 45th over.