The result lifts the Seagulls to 40 points, a usual benchmark to assure one's league status, while United must wait to ensure a second-place finish after a listless display.
They looked like strangers for too long, and, while the heavy rotation can explain that in part, this is a group of players most of whom have worked under Mourinho for two whole seasons now.
United thought they had an early lead when a free-kick from Anthony Martial was turned home by a deft touch from Marouane Fellaini, but the officials ruled he had strayed off-side.
United still need four points from remaining games against West Ham and Watford to be certain of finishing second.
Watch David de Gea's fine save from a long-range Glenn Murray effort in Manchester United's defeat at Brighton.
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 global on the edge of his own box moments later.
In what is a weird move from Jose Mourinho, Matteo Darmian and Marcos Rojo start for Manchester United in defence against Brighton. In the hardscrabble bottom half of the Premier League, the margins between success and failure, between survival and relegation, can often be thin, but rarely so literally as in this instance.
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.
Victory would have virtually guaranteed United second place behind champions Manchester City. Normally when you win these games it's because your goalkeeper has had to make saves and they've missed chances. Nemanja Matic, one of the most consistent midfielders in the league at the moment, will start alongside Paul Pogba in a two-man midfield for this trip to Falmer Stadium.