The Bantams got off to a flying start when Jack Payne opened the scoring after four minutes.
Goalkeeper Matt Macey parried George Miller's shot into the path of Payne and he fired home from 10 yards.
Argyle's response was swift as striker Freddie Ladapo stooped to head in his 11th goal of the season from Graham Carey's right-wing cross in the 12th minute.
City regained the lead six minutes later as Payne struck again, thumping the ball in off the underside of the crossbar after Macey had twice denied David Ball.
Argyle levelled in the 50th minute when Ladapo put Joel Grant in on goal. Grant's first effort was saved but he followed in to bundle the ball over the line.
Bradford took the lead for a third time when Miller latched on to Eoin Doyle's looped pass forward to make it 3-2.
But Ladapo again levelled following a goalmouth scramble from Carey's corner in the 74th minute.