The goals for the table-toppers came via Daniel Daly, Jake Topp and substitute Harvey Booth.
Carlton Athletic and Hall Green United shared the spoils after a six-goal thriller.
A Joseph O’Neil goal put Athletic ahead but Clifton Firth levelled matters up for United.
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Awais Akbar restored Athletic’s advantage, but goals from James Cusworth and Jamie Miller appeared to have handed United the three points, only for sub Nathan Kemp to rescue a draw for the hosts in the 87th minute.
Headingley AFC bagged three points after beating Boroughbridge 4-2 on the road.
The away side’s goals came courtesy of Joesph Cooper, Oliver Carter, Mark Freeman and Nick Gledhill, Jonathan Maullin hitting both for Boroughbridge.
Elsewhere in the top-flight, Huddersfield Amateur hammered Knaresborough Town 7-2 and a Paul Pyke brace guided Newsome to a 3-1 win at home to Whitkirk Wanderers.
Luke Gibson grabbed Newsome’s other goal, while Daniel Middleton netted for Wanderers, who were reduced to 10 men after Sebastien Brownrigg was sent for an early bath.
A solitary strike from sub Michael O’Brien was enough to help Field to a 1-0 win over Ealandians in the West Riding County FA Challenge Cup.
Joining Field in the draw for the next round will be title-chasing Ilkley Town, who beat St Bedes 2-1 thanks to goals from Tom Smith and Harry Brown.
Jamie Wasley smashed in four goals as Division One outfit Hartshead hammered Colne United 9-3 to progress.
Nathan Foster also smashed in a hat-trick and Jack Rodgerson hit a brace for the victors.
Goals from Henry Myers, Craig Nicholls and Oliver Nightingale guided Division One side Rawdon Old Boys to a 3-2 victory over Leeds Medics & Dentists, while Salts crushed Church Fenton FC 11-0.
Robin Hood Athletic progressed after beating Beechwood Santos 2-1, while Sherburn White Rose are out after losing 2-0 to Greetland.
Kirk Deighton Rangers thrashed Overthorpe Sports Club 9-2 in the West Yorkshire League Cup.
Charlie Yates hit two, with their other goals coming from James Woodward, Robert Holliday, Jack Holliday, Harjashun Bhandal, Luke Dubery and sub Josh Barden.
Division One leaders Campion had to settle for a 3-3 draw on the road at third-placed Glasshoughton Rock.
Goals from Jahro Parchment, Eli Petschak and Christopher Hellewell weren’t enough for the pacesetters as Robert Rice, Josh Prudhoe and John Adey replied for the hosts.
Shelley took full advantage as their 3-2 win over Otley Town saw them close the gap to two points.
Their goals came from Samuel Awty, James Bootland and Jacob Hawke.
Kippax leapt out of the relegation places thanks to a 4-2 win over Wyke Wanderers, who replaced them in the bottom two.
Thomas Micklethwaite bagged a brace for Kippax, whose other goals came from Aaron Gray and sub Ben Harley.
Ashley Andrews scored both of the goals for the Wanderers.
Two Josh Waite goals and strikes from Ryan Firth and Jack Farrimond helped Pool to a 4-2 win at Featherstone Colliery, Antonio Crnic and Joseph Threlfall on target for the hosts.
Kingston David smashed a hat-trick and Kyle Jeffrey was also on target as East End Park won 4-2 at Oxenhope Recreation, Daniel Moriarty and Ben White notching for Recreation.
Wetherby Athletic beat Aberford Albion 3-2, Joshua Wilson, Anthony Walsh and Jonathan Dockerty their goalscorers.
Division Two promotion-chasers Brighouse Sports Club Old Boys progressed in the West Riding County FA Challenge Trophy thanks to a 6-2 win over Tyersal.
Connor Durkin hit two goals for the victors, whose other goals were scored by Saxon Hargreaves, Hassan Ali, Luke Cranswick and sub Jack Whelan.
Harrogate Railway Athletic thumped Beeston Junior Reserves 17-0 to progress, while Huddersfield YM cruised to a 5-0 win at Altofts. Luke Peacock and sub Declan James hit two each and Darius McLeod was also on target.
Sub James McGlinchey hit two as Ripon City won 6-1 at AFC Illingworth St Mary’s Reserves and Danny Wiltshire was at the double to fire Swillington Saints to a 4-1 victory at Britannia Sports.
Nathan Hutchinson hit four as Kellingley Welfare hammered Oxenhope Recreation Reserves 8-4, while Old Centralions progressed thanks to a 3-2 win at Leeds City Reserves.
Rothwell dumped out Salem thanks to a 3-1 home win, while Shire Academicals Reserves also moved into the next round after beating Hunsworth 4-1 and Leeds Modernians beat Tadcaster Magnets Reserves 2-0.