It is a sign of the times for Championship outfit Pompey, who named just four substitutes due to their small squad, that they find themselves eliminated from a competition they have enjoyed such success in recently.
Having lifted the trophy under Harry Redknapp in 2008, they were beaten by Chelsea in the final at Wembley last time out.
But they have not made it beyond the third-round stage this year after Gus Poyet's League One leaders capitalised on Kitson's petulant sending-off to lead 2-0 for much of the game, courtesy of goals from Chris Wood and Ashley Barnes.
Tom Kilbey did pull one back for Portsmouth late on, but substitute Francisco Sandaza soon restored the two-goal margin to secure the Seagulls' place in the fourth-round draw.
Despite being in a lower division, the hosts went into the clash as favourites according to the bookmakers.
However, it did not show early on, with the class of David Nugent, Kanu and Liam Lawrence telling for Pompey during the opening exchanges.
The League One side were clearly rattled by the fast-paced nature of the football, although the visitors failed to fashion any clear-cut opportunities.
Despite struggling for possession, the Seagulls thought they had taken the lead in the ninth minute but Barnes, coming into the XI as one of six changes made by Poyet, saw his goal rightly ruled out for offside.
That seemed to spur the hosts on and they almost went ahead moments later when Elliott Bennett whipped in an excellent centre which Wood headed just wide.
Portsmouth's cause was not helped by the foolish behaviour of experienced striker Kitson in the 14th minute.
Having already been warned for petty pushing, the former Reading man ludicrously elbowed Adam El-Abd, leaving the referee with no choice to brandish a red card.
The one-man advantage took its toll just 12 minutes later when Mauricio Taricco's poor effort was deflected into the path of Wood, who fired home sweetly.
Not content with one, Brighton pushed for a second and nearly got it when Barnes saw his header rattle the crossbar after an excellent cross from Taricco.
It was all one-way traffic for the rest of the half and, after Jamie Ashdown brilliantly denied Murray and Barnes in quick succession, the Seagulls got their just rewards.
Pompey's ill-discipline again proved their downfall as Ibrahima Sonko inexplicably handled, allowing Barnes to convert the spot-kick.
Picking up where they left off, Brighton continued to dominate after the interval, pulverising Brighton with some champagne football to the delight of the home faithful.
They nearly grabbed a third midway through the half, but Barnes saw his wonderful 20-yard effort hit the side netting.
The hosts were more subdued thereafter, opting to control the game and, despite Kilbey's 88th-minute strike, they secured their passage into the next round through Sandaza's cool finish.