The Premier Division's leading marksman struck twice – taking his tally for the season to 29 – to help Hodnet secure a 3-0 win at home to Dawley Town.
Harry MacDonald joined Parker on the scoresheet as Hodnet stayed seven points clear of title rivals Shrewsbury Juniors.
Juniors, who won 4-1 at Prees United, still have their fate in their own hands thanks to the three games in hand they hold on Hodnet,
Ben Davies and Cal Routley both struck twice for Juniors.
Two goals from Ed Rogers and one from Zakh Ward saw Gobowen Celtic to a 3-2 away day win at Ludlow.
Callum Wilson was the star of the show in the clash between Newport Town and Morda United.
Wilson bagged a hat-trick to help Newport to a 5-2 success. Jordan Turton and Charles Carrick added to Wilson's haul with Jordan Gerrard and Adam Oliver replying for Morda.
Shrewsbury Up & Comers and Wrockwardine Wood Juniors shared the points following a 2-2 draw.
Alex Herbert and Ablay Sowe netted for the hosts with Ayden Preece and Michael Wood on target for visiting Wrockwardine.
A five-star showing from Danny Burke powered Albrighton a resounding victory at Dawley Town FC in Division One.
Burke hit the back of the net five times as Albrighton ran out 9-1 winners. Sam Edmondson added a double while Callum Higginson and Ed James netted once each. Mitchell Delamere grabbed a consolation for the home side.
Ercall Colts Juniors claimed a 3-1 success at home to Brown Clee.