Fowler’s first strike after 27 minutes was followed by a second two minutes after the break before Gareth Groves bagged Beeston’s third near the end.
Beeston remain the only unbeaten team in the Premier Division with eight wins out of nine and one draw leaving them three points clear of second-placed Ilkley Town and with a game in hand.
Ilkley kept up the chase with a 5-1 success at home to bottom club Sherburn White Rose as Ben Greenhow and Thomas Fleming both netted doubles.
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Harry Brown was also on target for Ilkley with Kyle MacDonald bagging a consolation for Sherburn who had Joseph Fella sent off.
Horbury Town climbed to third and one point behind Ilkley with a 4-1 triumph at home to Hunslet Club who dropped to fourth.
Gibral Bojang struck a second-half brace for Horbury after goals from Brad Ball and Luke Playford in the first half.
Fifth-placed Field saw their home clash against tenth-placed Boroughbridge postponed.
Elsewhere in the top flight, defending champions Carlton Athletic slipped to second bottom after a 5-0 hammering at home to ninth-placed Huddersfield Amateur.
Knaresborough Town jumped above Carlton to 13th with a 2-1 triumph at Hall Green United thanks to goals from Jack Carr and Craig Robinson as a Tom Fowler effort failed to save the 11th-placed hosts.
Robin Hood Athletic also leapfrogged Carlton and now sit 12th after their 4-2 win at home to seventh-placed Whitkirk Wanderers.
Billy Boseley-Yemm’s double was backed up by strikes from Daniel Bridges and James Finlayson for Athletic with Matthew Waller and Daniel Brown in the goals for Whitkirk.
In Division One, leaders Campion moved three points clear with a 4-1 victory at home to 11th-placed Aberford Albion.
Jahro Parchment bagged a brace for Campion who also had Zak Khan and Kyle Bingham netting with Dominic Blair the solitary scorer for Aberford.
Glasshoughton Rock moved second by edging a remarkable 7-5 goal feast at home to tenth-placed Wetherby Athletic. John Adey helped himself to four goals for Glasshoughton who were put in seventh heaven with Robert Rice at the double and Matthew Jenkins also netting.
Kirk Deighton Rangers sit third after a 1-0 win at home to Shelley as Joe Turley bagged the only goal of the game.
Otley Town – who now sit fourth – were on League Cup duty and suffered a 6-1 loss at home to Division One’s bottom club Oxenhope Recreation.
Rawdon Old Boys – who are sixth – were 3-0 winners at Division Two side Leeds Modernians while Hartshead lost 2-1 at fellow mid-table Division One side Salts.
Pool, ninth in Division One, obliged 4-2 at Division Two side Rothwell while a Kippax side who are second-bottom in Division One lost 4-3 at Kellingley Welfare who are fourth-bottom in Division Two.
Visitos Featherstone Colliery also lost out 4-1 in an all-Division One clash at East End Park.
Swillington Saints won an all-Division Two affair at Tingley Athletic 5-1, whilst Howden Clough progress 5-4 on penalties against visiting Altofts after a 1-1 draw.
In the sole regular Division Two fixture, Overthorpe Sports Club enjoyed a 2-1 win at home to Ripon City to move top.