For the first time in almost two years, Mourinho's men conceded more than twice with all three Brightongoals arriving before half-time through Glenn Murray, Shane Duffy and a Pascal Gross penalty.
Brighton took control in the first half-hour thanks to two goals in the space of 143 seconds, with Murray clipping a delightful finish past David de Gea before Duffy swept home after United failed to clear a corner.
That reprieve lasted just 10 minutes, however, before more rash defending by Bailly allowed Brighton to restore their two-goal lead when he brought down Gross, who converted from the spot.
Another is Watford, which beat Burnley 3-1 away in the other game Sunday.
Not long after that, the whistle went for half-time with Brighton in dreamland but United were in dire straits and were in need of a miracle in the second half if they were to get back in the game. Shane Duffy finishing after the ball fell to him following a corner that was needlessly conceded by a sluggish Eric Bailly.
Brighton pulled a big surprise against Manchester United on Sunday afternoon.
"The result shifts the mood from last week [a 2-0 defeat at Watford], but it doesn't change anything".
Brighton fought hard for survival in their first campaign following promotion last term, securing their top-flight status with a win against United in their final home match. In team news, club captain Bruno is absent with a thigh injury.
A club legend, Ryan Giggs would simply take a nanosecond to say "yes" were he offered the position of manager.
Only four teams managed to win at Brighton last season and it will be a hard place to play this season, too.
Mourinho then threw on Marouane Fellaini in place of Anthony Martial on the hour, but still United continued in listless fashion.
"It is Guardiola versus Mourinho once more; possession versus defence; attacking football versus "park-the-bus", Kingsley says during episode two, "Noisy Neighbours", as City's progressive style against Manchester United's negative football is highlighted. Lukaku could be in line for a start leading the line in Brighton.
Paul Pogba added a second goal for United before the end of the game but it was too little to late as the Seagulls held on for yet another impressive win against the Red Devils.
Pogba lined up on the left side of a three-man central midfield, with Andreas Pereira as the anchor man and summer signing Fred further right.
Manchester City vs. Huddersfield live stream
He reserved special praise for Mateo Silva , son of David, who appeared in his dad's arms as mascot prior to the match. Three points on Manchester City 6-1 Huddersfield in the Premier League on Sunday afternoon.