Hartlepool shook Bradford with a goal after 50 seconds.
Goalkeeper Richard O’Donnell failed to hold a shot from Gavan Holohan and Cullen seized on the loose ball to score from close range. Luke Molyneux went close to adding to Hartlepool’s lead when his angled shot flashed just wide of the far post.
Bradford enjoyed plenty of possession, but the nearest they came to scoring in the first half was just before the interval when Charles Vernam forced Ben Killip to make a diving save.
The Bantams pressed hard at the start of the second half to try to get back in the game, but they suffered another blow when Hartlepool increased their lead in the 60th minute with a close range header from Cullen.
Defender Paudie O’Connor gave Bradford hope when he scored with far-post header from Callum Cooke’s corner in the 72nd minute, but Hartlepool put the result beyond doubt with a third goal in the 90th minute, defender Yann Songo’o turning substitute Reagan Ogle’s cross into his own net. It completed a miserable night for City.
Bradford: O’Donnell, Threlkeld (Cousin-Dawson 61), O’Connor, Songo’o, Foulds, Watt (Robinson 77), Sutton, Gilliead (Lavery 61), Cooke, Vernam, Cook. Unused substitutes: Canavan, Kelleher, Evans, Scales.
Hartlepool: Killip, Sterry, Hendrie, Byrne, Ferguson, Shelton, Featherstone, Holohan (Fondop-Talom 85), Daly, Molyneux (Ogle 89), Cullen (Grey 70). Unused substitutes: Jones,Odusina,Crawford,Mitchell.
Referee: T Nield (West Yorkshire).