At the very least, the visitors will hope to mount a more impressive title challenge than they managed last season. Jose Mourinho's charges finished in second place but were 19 points adrift of runaway champions Manchester City.
As for the Seagulls, merely preserving their Premier League status would surely be regarded as an impressive achievement. Going by their performance in their opener away to Watford, Chris Hughton's side may face an uphill struggle to finish above the bottom three in May next year.
After some respectable displays in their pre-season games - including a 2-1 victory over Ligue 1 side Nantes - Brighton succumbed to a 2-0 defeat away to Watford at Vicarage Road last weekend, giving a dismal performance which left Hughton baffled and frustrated.
The Hornets' comfortable victory means that the Seagulls have now gone 14 Premier League away games without a win, a dismal run in which they have lost ten times on the road. However, Brighton's home record is far more impressive - as the Red Devils discovered to their cost last season (more on this later).
Meanwhile, United's pre-season record was rather mixed, including a 2-1 win over Real Madrid and a 4-1 hammering by bitter rivals Liverpool - although it should be noted that United were without numerous first choice players against the Reds.
Nevertheless, Mourinho's side made a solid (if unspectacular) start to their league campaign on Friday 10th August, as Paul Pogba shone in a 2-1 victory over Leicester City at Old Trafford.
Brighton brought in ten players in the transfer window, including Iran winger Alireza Jahanbakhsh, who joined from Dutch side AZ Alkmaar. Jahanbakhsh was top scorer in the Eredivisie last season with 21 goals.
Unfortunately for Hughton, two of his summer acquisitions will be absent on Sunday. Romania striker Florin Andone has groin, hip and pelvic issues, while goalkeeper Jason Steele has a thigh injury.
In addition, Colombia winger Jose Izquierdo is carrying a knee injury, while right back Bruno is ruled out with a thigh injury.
Mourinho also has several injury concerns, with five players definitely ruled out - midfielder Nemanja Matic, right backs Diogo Dalot and Luis Antonio Valencia, centre back Marcos Rojo and goalkeeper Sergio Romero. In addition, Ander Herrera has a tight hamstring.
However, the biggest concern for United fans is surely their manager's increasingly strained relationship with star midfielder Pogba. The France World Cup winner captained the Red Devils and gave an excellent performance against Leicester, but this was followed by an extraordinary public spat between Mourinho and Pogba.
Consequently, Red Devils fans will no doubt be relieved that Mourinho has now confirmed that Pogba will retain the captaincy against Brighton.
Potential Man Utd Starting Lineup: De Gea; Young, Bailly, Lindelof, Shaw; Fred, Fellaini, Pogba; Mata, Sanchez; Lukaku.
Potential Brighton Starting Lineup: Ryan; Montoya, Duffy, Dunk, Bernardo; Jahanbakhsh, Stephens, Propper, March; Gross; Murray.
Previous Encounter (May 2018, Premier League)
Brighton will hope to emulate their exploits in the equivalent fixture last season, when Pascal Gross headed home the only goal of the game. United centre back Marcos Rojo appeared to have cleared the ball, but it had already crossed the line.
The Seagulls' victory secured their Premier League status against a flat United side who didn't have much left to play for, with a UEFA Champions League place already guaranteed and Manchester City already crowned champions.
The game itself was unremarkable, but Mourinho was memorably graceless in the post-match interview. The Portuguese bluntly claimed that Marcus Rashford's disappointing performance in a centre forward role vindicated his preference for Romelu Lukaku - although, in Rashford's defence, he did force Mat Ryan to make a fine save at one point.
Brighton's superb win over the Red Devils last season came when they were still fighting for their Premier League lives. The threat of impending relegation often seems to inspire teams to achieve unlikely results against more illustrious opponents.
With the season still at such an early stage, it will be remarkable if the Seagulls are as impressive as they were in May against United. It will be even more astonishing if the Red Devils are as poor as they were in that game - especially seeing as they started this season strongly against Leicester.
A routine United win looks like the likeliest outcome.
Predicted Result: Brighton 0-2 Man Utd