FC UNITED chief Karl Marginson was left frustrated as the Rebels were held by 10-man Bamber Bridge.
Marginson's men dominated for long spells of a tense UniBond First Division North promotion battle.
Yet it was Brig who came closest to snatching an against-the-odds victory after they had been hit by Matt Mahoney's 59th-minute dismissal.
FC's best opportunity fell to Rory Patterson, but his superbly-struck free-kick was brilliantly saved by home keeper Terry McCormick.
"It was a useful point but under the circumstances, we'd have liked all three," Marginson said.
"We just didn't have enough about us to make the extra man count."
The Irongate stalemate keeps FC lurking dangerously in seventh place, while enabling Curzon Ashton to leapfrog Bamber Bridge into second.
Mike Norton and Jorge Diaz scoring in Curzon's 2-1 win over visiting Garforth, who were always off the pace.