The Bantams led three times, but failed to get over the line in a thrilling encounter at Home Park.
Jack Payne’s brace plus another goal from George Miller were cancelled out by Freddie Ladapo’s double and Joel Grant getting on the scoresheet.
City manager David Hopkin reflected: “It is frustrating. We scored three fantastic goals.
“It was two points lost. When they made it 3-3, you’re just hoping they don’t score again. There are things that are costing us at the moment.”
The Bantams flew out of the blocks as Payne picked up the scraps from George Miller’s parried shot four minutes in. But it was level eight minutes later when Ladapo powered home from Graham Carey’s cross.
David Ball was denied twice by Matt Macey before Payne regained the lead for the visitors with a crashing strike that hit the underside of the bar.
Richard O’Donnell made a fantastic diving save to deny Grant, but six minutes after the restart Plymouth struck as Grant levelled after an initial save.
Miller instantly hit back by latching onto Eoin Doyle’s long ball before coolly firing home.
Before the hour O’Donnell denied David Fox’s header with a superb stop. Lewis O’Brien wasted an opportunity when he was denied by Macey and, with 16 minutes left, Argyle came back once again through Ladapo.
At the finish, Miller was kept out by Macey.
Plymouth Argyle: Macey, Riley, Edwards (Taylor, 66), Canavan, Smith-Brown, Fox, Songo’o, Carey, Sarcevic, Grant (Lameiras, 77), Ladapo. Unused substitutes: Letheren, Sawyer, Grant, Wylde, Purrington.
Bradford City: O’Donnell, Caddis, O’Connor, Mellor, Chicksen, Henry (Akpan, 81), Ball, O’Brien, Payne (Colville, 87), Doyle, O’Brien, 69), Miller. Unused substitutes: Wilson, McGowan, Brunker, Devine.
Referee: R Lewis.