Promoted from the third tier last term, Daniel Marshall’s team thrashed Oxenhope Recreation 7-2 on the opening day of the season and were 3-1 victors over Rothwell at the weekend.
Roman Neal set Deighton their way with a strike on the hour-mark before Josh Barden’s late brace wrapped things up.
Sandwiched between those two triumphs was a 2-0 midweek defeat at Boroughbridge, Dominic Creamer and Chris Simpson grabbing the hosts’ goals.
The men from Aldborough Road then followed that result up with a 3-2 success over Newsome.
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Creamer and Simpson were on target once again, while John Rimmer also notched.
Elsewhere in the first division, Wetherby Athletic have endured a miserable beginning to 2018/19 and find themselves propping up the table following three successive losses.
The most recent of these came when they went down 3-1 at home to East End Park.
New manager Lewis Atkinson has made an instant impression at second division Ripon City, guiding the Mallorie Park club to a couple of resounding victories.
Their first fixture of the campaign saw them complete a 7-0 demolition of Knaresborough Celtic.
Hat-trick hero Jordan Atkinson, Adam Haswell (2), and Tom Cregan all struck, while an own goal rounded things off.
On Saturday, City got the better of Hunsworth by a 3-0 scoreline, Kyle Fox helping himself to a brace and Josh Coull netting the hosts’ third of the afternoon.
Celtic meanwhile, have struggled to date and are still looking for their first points of the season, three matches in.
Knaresborough Town Reserves kicked-off the season with a 3-1 Premier Division triumph over Horbury Town as Ben Dickens hit a double.
Steve Walker’s second-half finish earned a 1-0 win at home to Salts First next time out, but their 100 per cent record was ended on the road at Carlton Athletic on Saturday, the home team running out 3-0 winners.