Jamie Milligan made five changes to the side that defeated West Allotment Celtic 7-2 in the FA Cup first qualifying round on Saturday – and one of those changes played a key role in the opening goal of the evening on 10 minutes.
Rob Apter received the ball just inside the opposing half before embarking on a driving run into the penalty area.
From there, he unleashed an effort that was well saved by goalkeeper Cameron Belford, with Ewan Bange on hand to hook in the rebound for his seventh goal in seven games.
Apter then had another shooting opportunity on 13 minutes, this time seeing his long distance effort go over the bar.
Radcliffe equalised two minutes later when ex-Fleetwood man Bobby Grant produced a powerful header into the bottom corner of the net from a right-sided cross.
Grant then hit the post from a long-range free kick, before Bange saw a one-on-one effort well saved by the feet of Belford at the other end.
Belford was called into action again on 42 minutes to tip a fiercely-hit Danny Forbes volley over the bar.
The first clear-cut opening of the second half fell to the visitors on 51 minutes.
Defender Joseph Cummings rose highest to meet a corner from the right, with his header crashing into the upright.
Brig keeper Danny Roccia then saved from another Grant header, before Mark Yeates saw his strike take a wicked deflection at the other end and curl narrowly wide of the post.
With 68 minutes on the clock, Radcliffe were awarded a penalty.
Grant stepped up and had his effort well saved by Roccia, before the Brig keeper – and his defenders – made a series of vital blocks to prevent the visitors from taking the lead.
That wasn’t to be the last of the drama. Brig’s Matthew Flynn was shown a red card after bringing down Radcliffe substitute Kole Hall outside the area, before Grant fired the resulting free-kick over the bar.
Elsewhere in the division, Lancaster City were beaten 1-0 at home to Warrington Town, Joshua Amis getting the vital goal in the 63rd minute.