The Bantams finished 1-1 at full-time, but Michael Collins’s side found them wanting with their spot-kicks as the Silkmen claimed a famous midweek win.
Danny Whitaker netted first for the hosts from the spot but keeper Rhys Taylor saved Anthony O’Connor’s opening penalty.
Harry Smith had his spot-kick saved at the other end by Ben Wilson and then Hope Akpan equalised.
David Fitzpatrick put Macc 2-1 up but Joe Riley’s shot was saved by the on-song Taylor.
Michael Rose netted and Jack Payne scored to make it 3-2, before Tyrone Marsh bagged the winner.
Earlier, Fiacre Kelleher had given the hosts the lead on the hour mark with a clinical header.
But it took the Bantams just two minutes to get level when new signing Luca Colville scored on his debut.
The former Huddersfield Town winger penned a one-year deal with the club earlier in the day having impressed on trial.
Adam Chicksen and George Miller were both thwarted by Taylor, but Whitaker and Smith both wasted good chances for the hosts.
Macclesfield: Taylor, Fitzpatrick, Kelleher, Grimes, Wilson (Arthur 71), Smith, Welch-Hayes, Napa (Marsh 90+1), Maycock, Whitaker, Rose. Unused substitutes: Lowe, Blissett, Pearson, Simpson.
Bradford: Wilson, Riley, Chicksen, McGowan, O’Connor, Scannell, Payne, Miller (Brunker 70), Seedorf, Akpan, Colville (Wright 71). Unused substitutes: O’Donnell, Robinson, Gibson, Wood, Knight-Percival.
Referee: J Simpson (Lancashire).