Newark were many people's pre-season favourites for the title but they have had a few problems on and off the field and Glapwell took full advantage of that by getting off the mark.
Lee Naughton gave Glapwell the lead on 17 minutes when his cross from the right took a slight deflection and looped into the far corner.
Glapwell had the ball in the net twice as well with both times Josh Parfitt denied by an offside flag before Parfitt was also denied by the post.
The home side, themselves, were also denied by the woodwork as an effort from range came crashing back off the crossbar.
Glapwell's lead was doubled just after the hour when Ryan Cancellara's cross from the left dropped into the far corner.
Newark got themselves back in it, though, when Jake Reynolds lifted the ball over Ryan Hopkins from the edge of the area.
The two-goal advantage was regained, though, with 15 minutes remaining when Daniel Russell was tripped in the area with the referee playing a good advantage which allowed Josh Clayton a simple tap-in from six yards.
All-in-all a good start to the season for Glapwell who sit third after the opening weekend with a tough away game at Ollerton Town next weekend.
Full match report and photos to follow.