AFC Totton tore apart nine-man Bradford Park Avenue to progress to round two.
The visitors had Richard Marshall sent off before Jonathan Davies's drive and a Michael Gosney penalty made it 2-0.
Adam Clayton pulled one back from close range before a Michael Charles tap in, Gosney's neat strike and substitute Stefan Brown's finish made it 5-1.
Martin Drury then saw red for Bradford, but Totton showed no mercy as Brown scored twice to complete his hat-trick and Davies finished the scoring.
The Southern Premier Division side started brightly and their cause was aided by Marshall's red card for violent conduct.
Davies gave the hosts the lead when his angled cross-shot caught out visiting keeper John Lamb.
Gosney doubled their lead from the spot after Nathaniel Sherborne was fouled in the area by Ross Daly.
The hosts' celebrations were shortlived however as the Northern Premier Division side pulled themselves back into the tie when Clayton poked home Martin Drury's free-kick.
Charles reinstated Totton's two-goal lead when he swept home after neat approach play and Gosney completed his brace with a lovely finish from Davies's centre.
The influential Gosney then broke through the beleaguered Bradford defence before setting up Brown to make it 5-1.
Drury's red card for a second bookable offence moments later left the Avenue hanging on for the final whistle.
The hosts were not in a charitable mood however and Brown finished Mark Osman's cut-back before notching his treble after a flick-on from fellow sub Osman.
Davies ended the rout with a firmly struck left-footed effort from the edge of the box in the last minute.
VIEWS FROM THE DRESSING ROOM
AFC Totton manager Stuart Ritchie told BBC Radio Solent:
"I thought it would be a tight game and they are a good side but our effective players really hurt them and they couldn't handle us.
"I'm so proud of the whole club, it's a massive achievement and long may it continue.
"Hopefully we can get a good draw, get the cameras in and bring some serious money in."