Two Notts County goals either side of the interval put paid to Bradford's cup ambitions at Meadow Lane and ensured Sven-Goran Eriksson would have an interest in the second-round draw.
County have been in the headlines for their big-budget plans to join English football's elite, and a run in the FA Cup could give them a taste of the big time ahead of schedule.
After a tight first period County took the lead on the stroke of half-time when Karl Hawley swept home a right foot shot, and almost immediately from the re-start Johnnie Jackson made it two.
County continued to have more of the chances and although Bradford reduced the deficit through Michael Boulding in the 81st minute they could not push forward for a crucial equaliser.
David Connolly's second-half debut double helped Alan Pardew's Southampton see off Bristol Rovers in tonight's FA Cup first round despite a spirited late comeback by the home side.
Connolly, making his first start after joining Saints as a free agent, broke a tense deadlock in the 63rd minute when he swept home a left-footed effort from Adam Lallana's cross to put the in-form visitors in front.
And just five minutes later Connolly effectively booked the 1976 Cup winners' place in round two when he placed another low shot past Rovers keeper Rhys Evans from a Michail Antonio cross.
Antonio added a third for Saints two minutes later after a long ball forward from Richard Lambert.
Rovers kept pressing and a goal from Darryl Duffy and a Jeff Hughes penalty ensured some anxious final moments for the visitors.
League Two promotion hopefuls Dagenham and Redbridge proved no match for Huddersfield who hit the Londoners for six before a late consolation from Paul Benson gave the visitors something to shout about.
Robbie Williams opened the scoring in the ninth minute from a free-kick after a handball by Peter Gain, Gary Roberts headed a second on 21 minutes and Lee Novak struck his first of the night three minutes later.
The contest was all but over by half-time thanks to Jordan Rhodes' strike just before the break, but the Terriers kept pressing and further goals from Novak (56) and Roberts (72) wrapped up an emphatic win.