Thackley built up a good lead at home to struggling Northern Counties East League opponents Parkgate and were glad of their four-goal cushion as the visitors snatched two late replies.
Damian Hopkins headed the Dennyboys in front early on but picked up an injury and had to be substituted on the quarter-hour mark.
Mike Garrod and Paul Whiteley made it 3-0 before the interval and Garrod added his second goal in the second half.
Parkgate pulled one back when Oliver Graham netted an 88th-minute penalty and George Morley made it 4-2 a minute later.
Also in the Premier Division, Brighouse Town suffered a 2-1 defeat at Worksop Parramore.
The home side took an early lead through Sam Smith. James Hurtley levelled but seconds later Smith put the home side back in front and he missed out on a hat-trick as Town keeper Jacob Giles saved his late penalty.
Albion Sports and Liversedge are in action tomorrow night with away games against Staveley MW and Winterton Rangers respectively.
* Farsley edged through to the fourth round of the Evo-Stik League Cup with a nervy 1-0 home win over Bamber Bridge, a scrappy own goal just after the hour seeing them through.