Bamber Bridge were forced to settle for a point, as they were held to a 2-2 draw at home to Droylsden.
The hosts led going into the break, but two goals late in the second half from the visitors turned things around.
However Brig rallied again and levelled the score from the penalty spot with ten minutes to play, to earn a share of the spoils.
It was almost the dream start for Brig when Matt Dudley raced through on goal in the first minute, but a strong hand from Branagan turned it behind for a corner.
The hosts started the livelier and James Boyd was the next to find an opening, but Branagan was out quick to smother his chipped effort.
Droylsden grew into the game more and on 10-minutes Sefton Gonzales called Rigby into action with a header at the far post, but it was comfortably saved.
Gonzales was in the action once again eight minutes later, but Rigby was on hand to parry his strike away.
Brig captain Michael Potts had a glorious chance to open the scoring on 25 minutes, but he steered his header from Dudley’s deflected cross inches over the bar.
Danny Forbes was forced off on the half hour mark after taking a knock, with top scorer Brad Carsley his replacement.
With half time approaching Brig found the back of the net through Carsley, who marked his return from injury with a bang.
Alistair Waddecar’s header was superbly saved, but Carsley was there to drill home the loose ball into the bottom corner.
HALF TIME: Bamber Bridge 1-0 Droylsden
The visitors made one change at half time, with Ben Barber making way for Shaun Holden.
It was the trailing side that started the brighter, with Rigby forced into two saves in close succession in the opening five minutes of the second half.
Kilheeney saw a snapshot gathered, before Rouse’s shot at the near post was well blocked.
On 53 minutes Kilheeney came even closer, as the captain’s well struck shot clipped the top of the crossbar.
On the hour mark Regan Linney worked an opening after fantastic footwork, only to see his low effort turned behind for a corner.
The pressure eventually told when the ball broke to Liam Caddick inside the box and the winger struck the ball into the back of the net on the half volley.
Five minutes later it got even better for the visitors, when Caddick arrived in the box to guide home the cross into the bottom corner.
The response having fell behind positive from Neil Reynolds’ side and they were gifted the chance to equalise when Waddecar was hacked down inside the box.
Substitute Jamie Milligan stepped up and slotted the ball home into the bottom left corner to set up an exciting last ten minutes.
The hosts really piled the pressure on the visitors and on 88 minutes Branagan produced a remarkable save to keep out Carsley’s powerful header.
Adam Dodd was the next to see his strike saved – Branagan tipping his venomous left footed effort behind for a corner.
That draw sees Brig make it four points in four days from two tough games, as they aim to take their unbeaten momentum into the trip to fellow high flyers Hyde on Saturday.
Match reporter: George Hodgson @ghodgsonsport