Pools went into the game without a win this campaign but ripped the Bantams apart, with three second-half goals coming in 10 minutes.
The visitors did not trouble Hartlepool all night as they conceded five goals for the first time since losing to Swansea in last season's Capital One Cup final.
Pools had only one goal in six games to their name this season, but after Luke James headed them in front after 24 minutes, they never looked back.
"The first goal was vital," said Cooper. "It gives you extra belief in what we are trying to do.
"We wanted to do it simple. Bradford are normally 4-4-2, we stuck to our jobs and roles. First ball or second ball, win it and play your football.
"We say it's been coming, but it did in this game. All the basics and cornerstones - effort and application - were all there.
"After the first goal we saw some young people, and old, grow. We created chances, lots of them, and we should have been three up at half-time."
Pools added second-half goals through Jon Franks three minutes after the restart, Christian Burgess in the 56th minute and Jack Compton from the penalty spot two minutes later. Nialle Rodney, a former Bradford striker, completed the rout with two minutes to go.
Cooper added: "To be one-up gives us a boost, something to hang on to. Then, early in the second half the goal gave us a lift and, from then on in it was a case of how many. I cannot be any happier than I am now."