The theme tune to the World War II movie The Great Escape also rang around the stadium as the players celebrated after an epic effort.
With third-bottom Southampton and 17th-placed Swansea to meet on Tuesday, Brighton now can't be relegated.
Man United still sit second on the log with 77 points after 36 matches.
Marcus Rashford, Anthony Martial, Juan Mata, Marouane Fellaini and Matteo Darmian all earned recalls, but the United boss blasted their contributions. I know we can do it, we only have two matches to get the four points we need.
At the other end Lewis Dunk bravely put his head in the way of a powerfully struck effort from Rashford, but then presented possession to the English worldwide on the edge of his own box moments later. United, meanwhile, have now lost away from home to all three promoted teams in the same season for the first time.
It is quite an achievement for Hughton, who guided Brighton into the Premier League for the first time last season, and for a club who 21 years ago this week needed a late equaliser at Hereford to save themselves from dropping out of the Football League altogether.
Glenn Murray, Pascal Gross, Jose Izquierdo, and goalie Matty Ryan have the quality to perform well enough for another full season and keep Brighton above the Championship.
Mourinho insisted it is "important" to ensure they finish as runners-up to Manchester City but accused his players of not feeling the same way. "They felt the game with different emotions", added Mourinho. They had one target, to get the points and celebrate their Premier League survival.
Brighton nearly doubled their lead when Izquierdo aimed just wide after United failed to clear a corner, before Juan Mata whipped a free-kick over the crossbar to prompt Mourinho into sending for substitutes Luke Shaw and Jesse Lingard.
Sanchez and Lukaku will come back in against Antonio Conte's side while Lingard, on the bench at the Amex, is likely to start, too.
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