After dominating the encounter for 75 minutes, Brain fluffed a simple clearance to present 18-year-old substitute David Brown with an open goal on his debut.
Seven minutes later, Bantams keeper Scott Loach handed out a lesson with a brilliant double save - first palming wide Terry Dunfield's penalty before blocking the powerful return from Neil Ashton after Danny Thomas had been upended by Joe Colbeck.
Macclesfield had carved out the better chances throughout the game with Levi Reid heading wide on four minutes as the home side dominated the opening exchanges.
Bradford's first chance came on 21 minutes when veteran striker Peter Thorne clipped a 20-yard drive inches over the bar.
The Silkmen side should have scored on 35 minutes when Michael Symes ghosted in behind his marker only to fire a left-foot shot inches past the far post.
Striker Martin Gritton then sent a weak header straight at Loach.
Symes had further chances to break the deadlock after the interval by first forcing a fine diving save from Loach with an eight-yard header, before flinging himself at a diving header in the 72nd when he would have done better to control with his feet when only six yards out.
After Loach's double save, Macclesfield threw all their men forward but they were denied by Bradford's strong defence.
Macclesfield, on the other hand, have only recorded two home wins all season and, although they have performed well against top of the table teams away from home, they have not won in front of their own fans since November 6.