Power struck in the ninth and 68th minutes and Horsforth’s other goals came from Joe Tasker, Joe Fitzpatrick, Mitchell Cameron and Charlie Yates.
Horbury lost their lead at the top after they could only draw 2-2 at basement-side Whitkirk Wanderers.
Gibril Bojang and Jak Kelly were on the scoreboard for Town while Duncan Dike and Willfred Frimpong replied for Wanderers.
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Hall Green United moved up to joint third spot, level on points with opponents Beeston St Anthony’s following a 2-1 home win on Saturday.
Jamie Miller and James Cusworth netted the goals for United.
Knaresborough Town also sit in joint third on 16 points following their 4-2 victory over Headingley AFC.
Hunslet Club picked up their first victory of the campaign thanks to a 2-1 verdict at Robin Hood Athletic.
Ashley Beck and Samuel Kyeremeh scored the goals.
Boroughbridge moved off the bottom of the table thanks to a 4-2 victory over Gomersal and Cleckheaton.
Elsewhere in the top division, Rawdon Old Boys drew 1-1 with Kirk Deighton Rangers and Huddersfield Amateur defeated Carlton Athletic 4-1.
In Division One, leaders Silsden picked up their seventh win in eight games thanks to a 2-0 home triumph over third-placed Shelley.
Ben Clarkson and Jacob Seward netted for Silsden who are six points clear of their opponents and four other chasing teams also on 15 points.
Albion crashed to a 4-0 defeat at Pool as Scott Higgins bagged a brace with Jack Farrimond and Nicholas Bulcock also contributing goals. Pool are now also up to joint second place.
Harry Hawking and Greig Hudson scored the goals as Otley Town moved level with their opponents East End Park on 15 points after a 2-1 victory.
Daniel Omosebi netted Park’s consolation goal.
A brace from Kyle Pearson helped Featherstone Colliery pick up their third victory of the season – 4-2 at Salts.
Swillington Saints Welfare moved up to 14th spot following their 3-2 home win over Wyke Wanderers.
Matthew Marshall gave the hosts the perfect start with a goal in the first minute and first-half strikes from Kieran Turnbull and Thomas Day put Saints beyond reach despite Louis Sterling’s brace for Wyke.
Elsewhere, seventh-placed Brighouse Sports cruised to a 4-0 victory at next-to-bottom Sherburn White Rose and Steeton were 2-0 winners over Wetherby Athletic.
Joshua Senior netted a hat-trick as Altofts continued their fine start to the season in Division Two with a 5-0 victory at FC Sporting Keighley.
Dillon Connelly and Reece Farnhill got the other goals.
Altofts’ nearest rivals Huddersfield LH could only draw 2-2 at Old Centralians while third-placed Rothwell Juniors suffered a chatening 5-0 defeat at Tingley Athletic.