Shields, who are playing catch-up in the league after their cup exploits, have three games in hand on Brig and are level on 33 points after both won 3-1.
Another fantastic crowd of 1,773 at Mariners Park saw Shields take the lead against fellow league newcomers Atherton Collieries just before half-time through Rob Briggs.
Glenn Matthews swiftly levelled for Colls immediately after the break but Briggs` second just shy of the hour-mark restored the hosts' advantage which they stretched in the very last minute through Jamie Holmes.
Brig beat Tadcaster Albion by the same score at Irongate in front of a decent crowd of 308.
And they had to come back from a 37th minute Tom Corner goal down to win. Brad Carsley bagged a quickfire brace shortly after half-time to put the home side ahead and Regan Linney confirmed the points with a 74th minute third for Neil Reynolds' side.
Scarborough Athletic are third, four points behind but having played just one fewer than Shields.
They won 2-1 at the Flamingo Land Stadium in front of another excellent crowd of 953 against Ramsbottom United. Michael Coulson gave Boro a 16th minute lead that Max Wright doubled 10 minutes later.
Rammy stopped the flow and it was 2-0 at the break, with the visitors reducing the arrears 11 minutes into the second half through Josh Heaton. But they weren`t able to find a leveller and Boro held firm for the points.
Glossop North End, Prescot Cables and Hyde United – on Emirates FA Cup duty of course – make up the rest of the play off positions.
Cables are there due to winning 3-2 at Glossop, who led through Callum Chippendale`s goal on the half-hour mark.
And when Tunde Owolabi doubled the Hillmen`s lead with only 17 minutes to go, it didn`t look good for Cables. But three goals in seven minutes shortly after that from Lloyd Dean with two and Jordan Wynne turned the game on its head.
Droylsden are just a point outside the top six after winning 2-1 at Llanelian Road against Colwyn Bay.
Liam Caddick broke the deadlock to give the Bloods a 48th minute lead that Danny Andrews cancelled out 10 minutes later. But Ciaran Kilheeney made it 2-1 to the visitors just past the hour-mark with what proved to be the winner.
Ossett Town are a point and a place further back after stalling after a 2-2 draw at Clitheroe.
The home side took an early 8th minute lead through George West and added a second from Brad Carroll seven minutes later. Alex Peterson crucially pulled one back 10 minutes before half-time. But it wasn’t until stoppage time at the end of the game that Ossett pulled level through recent signing Emile Sinclair.
Bottom side Goole AFC picked up a point from a 1-1 draw at the Victoria Pleasure Grounds against Radcliffe FC.
The Vikings couldn`t have asked for a better start as Carl Stewart gave them a first-minute lead. James Hooper eventually equalised in the 65th minute.
Skelmersdale United picked up a useful 2-1 Stormy Corner win over Mossley AFC with goals from Andy Owens after 18 minutes and Callum Mahoney on 31 minutes – Caldon Henson replying five minutes into the second half, while Colne picked up a fourth win of the season to date to move nine points clear of Goole.
The Lancastrians beat Kendal Town 2-1 at Holt House, thanks to Alex Curran after 11 minutes and new loan signing from Altrincham, Sean Miller, six minutes from time after Richard Seear had levelled on 56 minutes.
Third-bottom Brighouse Town were beaten 2-0 at home by Trafford, for whom Aaron Burns after 23 minutes and Steve Mason six minutes into the second half were the scorers.
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