Since his arrival in the summer of last year, Ten Hag has had the resounding support of United supporters, and the majority is standing behind the Dutchman in his latest altercation with winger Jadon Sancho.
But they made it clear that they disagreed with Ten Hag's choice to substitute Anthony Martial for new acquisition Rasmus Hojlund 19 minutes into the second half, as a cacophony of boos rang out around the stadium before the Dane was booed out.
Danny Welbeck, a former home favourite, scored in the first half to put United behind. The goal was followed in the second half by strikes from Pascal Gross and substitute Joao Pedro, both of whom were given far too much room near the United penalty box.
With their first United goal, Hannibal Mejbri gave the home team some optimism, but in a frantic end, it was the visitors who came closest to scoring again. Andre Onana made four outstanding saves, the best of which came in stoppage time to prevent Ansu Fati, a player on loan from Barcelona, a goal on his debut.
United had not lost at home in 13 months when Brighton won this game once more. The Seagulls have now defeated their opponents four times in a row in the Premier League, and this triumph drew additional jeers at the final whistle, but not quite as many as when Hojlund was substituted.
Ten Hag's team has now given up 10 goals in their last four games, marking the first time since 1979 that they have lost more than one game in a row.
Their poor start in the first five games dates back to the 2014–15 season under Louis van Gaal, when they collected six points.
In addition to the three devastating losses they suffered, Sancho, who is training separately from the first squad after claiming on social media that he felt Ten Hag was using him as a scapegoat in an obvious challenge to the manager's authority, is not present.
Additionally absent is fellow winger Antony, who was given time off to respond to claims made by his ex-partner.
Ten Hag is obviously having trouble with a number of his players unavailable, even with recent additions Mason Mount and Sofyan Amrabat watching from the stands.
Even so, United displayed a wealth of expertise, but aside from Marcus Rashford, their offence lacked much bite.
The England forward also provided the low cross that Hojlund, sliding in, likely should have converted in the first half after having one attempt diverted onto the angle between post and crossbar.
A goal at that juncture, when the score was still 0-0 and United had made a promising start, might have been crucial.
As it was, the home team's impetus quickly waned and there was no repetition of their heroics from last month when they overcame a two-goal deficit to defeat Nottingham Forest.
Even though Ten Hag's team is still considered to be in the midst of a reconstruction, it is important to keep in mind that the Dutchman has been in command of his squad longer than Roberto De Zerbi has at Brighton.
The contrasts between the two sides in that regard are obvious.
While only one of De Zerbi's signings, former Borussia Dortmund midfielder Mahmoud Dahoud, started for Brighton, six of United's starting lineup were acquired during Ten Hag's tenure.
Owner Tony Bloom said this week that De Zerbi's tactical prowess and attention to detail have taken him by surprise and that they have clearly had a significant influence.
But there is a continuity and vision behind Brighton that those in charge at Old Trafford would do well to take note of through Bloom, chief executive Paul Barber, captain Lewis Dunk, and beyond.
Like so many others in recent years, Simon Adingra is another player who was once 'unknown' but is now having a major influence for the Seagulls this season.
The Ivorian was acquired from Danish club Nordsjaelland last year and loaned to Bloom's Belgian club Union Saint-Gilloise before coming back for the current season as a more skilled player.
The 21-year-old found space on the left side of the home team's defence and crossed the ball; Adam Lallana deflected it, giving Danny Welbeck space to finish.
Before heading back to the south coast, Kaoru Mitoma took the Brighton to Union SG loan route as well. The effect of the Japanese striker has now been clear, and it was his ball that allowed Tariq Lamptey to find Gross for Brighton's second goal. The German's goal was made slightly simpler to score by Lisandro Martinez's unsuccessful dive to win possession inside his own area.
These are truly historic times for Brighton with star player Ansu Fati making his first club appearance in the dying seconds and another European debut set for Thursday against AEK Athens.