Brighton were 4-0 up by the interval and although Bognor picked up after the break, they were never going to get back into it – especially after skipper Harvey Whyte had been sent off soon after the start of the second halff.
It was sobering stuff for the Rocks, who must now lift themselves to try to get their Isthmian premier promotion bid back on track and can aim to do so without any further distractions in cup competitions.
Bognor gave debuts to new signings Tom Dinsmore and Jerry Puemo in defence and midfield after recruiting the pair at the end of last week. Another new recruit, winger Tresor Shema, was on the bench.
The game was a repeat of last season's semi-final at Sussex FA HQ, where a very young Brighton side were beaten 5-1.
But it was Brighton – on this occasion fielding a much more experienced line-up, with a number of young stars having faced Aston Villa in the League Cup earlier in the campaign – who drew first blood this time when, just four minutes in, an Archie Davies cross was deflectd into the net past keeper Amadou Tangara, possibly with frrom Lorent Tolaj getting a touch.
Brighton looked lively in the opening stages with Bognor struggling for possession. It was 2-0 on 12 minutes when Warren O'Mora surged forward and played Archie Davies free, and when he crossed Jordan Davies took a touch then shot powerfully past Tangara.
Jordan Davies almost had his second four minutes later when another quick passing move found the Bognor defence wanting but this time his shot was just wide. Then Tolaj found space for a low effort that Tangara saved.
It got worse for Bognor on 24 minutes when left-back Alex Cochrane's high ball in from the left took a deflection to deceive Tangara and nestle in the back of the net. It was four on 30 minutes when Peter Gwargis headed in Cochrane's cross when it found him unmarked after a run to the near post.
The worry at this stage was how many were Bognor going to let in. Bognor were finding very little chance to get at the Seagulls and Brad Lethbridge's 35th minute shot, well hit but in the end well wide, was their first real shot towards goal.
It ought to have been 5-0 on 41 minutes but Tolaj shot wide from close range after yet another good cross from the right by Archie Davies.
Gwargis appeared to twist his knee in a harmless chase for the ball towards the end of the first half and was replaced for the start of the second period by Jack Leahy, while O'Hora was replaced by Romaric Yapi.
Dan Smith headed a rare Rocks chance towards the bottom corner soon after the restart but keeper Adam Desbois clawed it out. At least Bognor had started the second half with more purpose.
On 52 minutes there was a Bognor debut for Shema as he came on for Matt Casey.
If Bognor's task wasn't already tough enough it got tougher when Whyte was shown a straight red for kicking out at Brighton's Jack Spong after a foul on a Rocks player halted a Seagulls attack. The home fans couldn't believe what had happened, especially as Whyte had only just returned from a ban after a previous red card. He is likely to be banned for three games, starting with next Wednesday's trip to Lewes.
Tommy Leigh came on to fill the midfield void caused by Whyte's dismissal. But Brighton soon made it five, Tolaj running on to a pass through the centre and belting a shot past the helpless Tangara.
Bognor almost pulled one back straight away but Keaton Wood's header came back off the bar and Shema couldn't quite touch in the rebound.
Sam Packham replaced Lewis Freestone for Brighton, before Lethbridge wriggled in the box to find space for a shot that was hacked off the line. At the other end Leahy's run ended with a shot that rattled the bar.
Ben Mendoza came on for Dinsmore, who'd had a tough debut but had looked classy in places. Then Lethbridge shot across goal and wide from close range after getting himself into a good position.
Suddenly the ten men of Bognor looked much brighter in attack and Tommy Leigh curled one narrowly wide from 22 yards. Shema was looking very lively and causing problems, striking one close-range shot into the side netting after a nice bit of footwork.
As the rain swirled around, it was six on 74 minutes when sub Yapi seized on a slip by Puemo to run through, round Tangara and score in the empty net.
Immediately Bognor woke the home fans up with a goal of their own, Josh Flint with the strike. And ten minutes from time Lethbridge got a second for the Rocks with a fierce shot from 15 yards that simply beat Desbois for power at his near post.
If any Bognor fans were dreaming of a very unlikely comeback, which in fairness they probably weren't, Tolaj nipped such thoughts in the bud when he slid Brighton's seventh under Tangara.
A Bognor break by Lethbridge and Tommy Leigh ended with the Pompey forward shooting low but too close to Desbois. Brighton, oddly, were looking shaky at the back and more than once the Rocks might have found a third but that was where the scoring ended.
The Rocks get back to league action at Haringey on Saturday while Brighton go on to play Worthing in the cup semi-finals in early March.
Rocks: Tangara, Kavanagh, Puemo, Dinsmore, Casey, Wood, Whyte, A Leigh, Smith, Flint, Lethbridge. Subs: T Leigh, Sherma, Mendoza, Wakley, Baker.
Brighton: Desbois, A Davies, Cochrane, Roberts, O'Mora, Freestone, Spong, Jenks, Tolaj, J Davies, Gwargis. Subs: Yapi, Leonard, Leahy, Packham, Keio.