Evan Ferguson showcased his burgeoning talent by scoring a superb brace after the half-time interval, with the visitors already trailing 1-0 to Deniz Undav's simple finish inside the opening six minutes on the south coast.
Wingers Solly March and Kaoru Mitoma added more gloss to Robert De Zerbi's side's victory with a goal apiece during the final 10 minutes of normal time, but it was not a scoreline which flattered the hosts, who were dominant throughout.
After becoming the first fourth tier side since 1990 to reach the quarter-finals of the FA Cup, Grimsby were aiming to make history by becoming the only one to ever make it to the final four of England's most historic cup competition.
However, Paul Hurst's side began life at the Amex Stadium in the worst possible manner less than six minutes into the encounter, with Undaz easily dispatching a rebound after the visiting goalkeeper Max Crocombe had spilled Moises Caicedo's effort from distance.
As expected, the Seagulls controlled the majority of the match with their patient possession and neat interplay, although their casualness almost got the better of them when Lewis Dunk's backpass looped over Robert Sanchez's head, but the Spain goalkeeper was able to sprint backwards and retrieve the ball inside his own six-yard box.
Undav and Mitoma both squandered presentable chances to double the hosts' lead before the break, but the Mariners somehow managed to hold on until the half-time interval, with their dreams of creating history remaining in tact.
They did not last long, however, when teenage sensation Ferguson doubled the Premier League side's lead only six minutes after the break. The 18-year-old expertly controlled Alexis Mac Allister's pass before quickly moving beyond his marker to fire the ball into the bottom corner.
The Republic of Ireland forward added to his growing reputation within the game to double his tally in the 70th minute, receiving the ball from his fellow goalscorer Undav before accurately dispatching the ball beyond the reach of Crocombe once again.
Despite Ferguson's strikes essentially ending the already understandably one-sided affair as a genuine contest, the work ethic which Roberto De Zerbi has instilled within his team since replacing Graham Potter last September was clear for all to see, as his side continued to press for a fourth during the latter stages.
After March achieved exactly that by meeting Adam Webster's inviting cross with a diving header, Mitoma scored the fifth and final goal of the match in the last minute of normal time, with the Japan winger's effort from distance deflecting off Luke Waterfall's legs and into the bottom corner.
For Grimsby, this season has already provided more than their fans could have dreamed of having also secured survival following their promotiond from the National League via the play-offs last season, while Brighton remain firmly in the hunt for achieving Champions League qualification and their first ever major trophy.