While the result for the Red Devils was disappointing, battling back from a goal down with 11 minutes left to play, they were give a big boost by the return to action of Ashley Young and Luke Shaw after missing three and four months respectively.
As hinted by senior boss Jose Mourinho last week, Shaw and Young were both used from the off, but neither could make any real difference during a flat opening hour to the contest.
The three-minute stoppage in play appeared to have an effect on United's game, as they struggled to create too many openings in the remainder of the half.
The closest they came to a breakthrough from open play arrived 33 minutes in when a shot from the edge of the box deflected off Scott McTominay and ended inches wide of the target.
Prior to their goal, Swansea spent large parts of the evening defending with a couple of wayward shots thrown into mix, the best of which saw Baker-Richardson fire into the side-netting after shrugging off Axel Tuanzebe.
It took until eight minutes into the second half for the visitors' first shot on target to arrive, but when it did it proved to be a real cracker as Gorre - on United's books for 11 years earlier in his career - picked out the far corner.
Gorre was given time to cut inside onto his left and, despite the angle being against him, caught Joel Pereira completely by surprise to haunt his former club.
Mitchell clipped the crossbar with a left-sided cross moments later and Gregor Zabret did well to latch on to Tominay's overhit touch before he could get a shot away soon after.
It was proving to be a disappointing evening for United, however, with Baker-Richardson coming close to adding a second for the Swans when blasting right at Pereira following an Aaron Lewis pass.
That all changed 11 minutes from time thanks to Boonen's maiden strike at this level, keeping his cool to lift the ball over Zabret when the ball fell nicely into his path six yards out.
United enjoyed far more possession from that point on but Swansea were given plenty of chances to counter, seeing substitute Liam Cullen and George Byers both squander late openings, though in the end they were happy to pick up a first point of the season.