Pools had only scored one in six games going into the tie, but turned the hapless Bantams over with ease.
After visiting defender Rory McArdle flashed a header wide after 20 minutes, Pools took the lead two minutes later.
Jon Franks' deep cross was headed back across goal by Jack Compton and Luke James nodded in from eight yards.
The home side had to wait until the second half for their second, but then nabbed three in 10 minutes.
After Franks' shot was blocked, he collected the rebound and fired past debutant goalkeeper Connor Ripley from 18 yards in the 48th minute.
A Compton free-kick was met by Christian Burgess who headed in a first career goal from close range after 56 minutes.
And in the 58th minute James was felled in the area by Nathan Doyle and Compton firmly struck home the penalty.
The rout was complete with two minutes remaining as Franks crossed for substitute Nialle Rodney to spectacularly net an overhead kick.