Van Gaal was taking charge of his first competitive game as United manager, but his new side exhibited many of the same failings from last season – when they finished seventh – as they slumped to a surprise defeat.
South Korea midfielder Ki Sung-yueng exploited inattentive marking to give Swansea a 28th-minute lead with a left-foot shot from the edge of the box.
United’s new captain Wayne Rooney equalised early in the second period, but Gylfi Sigurdsson condemned the hosts to a first opening-day home defeat since 1972 with a close-range finish in the 72nd minute.
It gave Swansea back-to-back wins at Old Trafford, following their shock FA Cup success in January, and was a reversal of United’s 4-1 win at the Liberty Stadium on the first day of last season.
“It is very disappointing that we have lost our first home match,” said Van Gaal, who took over at United after leading his native Holland to the World Cup semi-finals.
“We were very nervous in the first half, made the wrong choices, and that is a pity. In the second half, we never played as a team. Therefore, I’m responsible.”
Injuries obliged Van Gaal to give competitive debuts to Tyler Blackett, 20, and 21-year-old Jesse Lingard, who took their places in the 3-4-1-2 formation that had served United well in their unbeaten pre-season campaign.
Lingard’s day was to last only 24 minutes, however, as he was forced off after appearing to jar his knee in a challenge with visiting captain Ashley Williams.
United bossed possession in the first half, but Swansea struck from their first sight of goal, with Ki stroking home a lay-off from Sigurdsson.
– Sigurdsson crowns return –
Swansea’s fans burst into a chorus of ‘You’re getting sacked in the morning!’ aimed at Van Gaal, who sat impassively in his seat in the dug-out.
The Dutchman introduced Nani in place of striker Javier Hernandez at half-time, with the hosts switching to a 4-2-3-1 system, and United responded immediately.
Juan Mata’s right-wing corner was flicked on by Phil Jones and Rooney hooked home a spectacular close-range volley at the back post.
Rooney came close to putting United ahead with a free-kick that hit the outside of the post in the 66th minute.
But it was Swansea who claimed the winning goal when Icelandic midfielder Sigurdsson — back at the club after two years at Tottenham Hotspur — slammed home from Wayne Routledge’s mishit volley.
Later on Saturday, last season’s FA Cup winners Arsenal will begin their campaign at home to Crystal Palace.
With manager Tony Pulis having left Palace on Friday after a reported disagreement with co-chairman Steve Parish, assistant coach Keith Millen will be in temporary charge for the trip to the Emirates Stadium.
Elsewhere, Championship winners Leicester City will play their first top-flight game since 2004 when they host Everton, while fellow promoted side Queens Park Rangers welcome Hull City to Loftus Road.
In the day’s other games, Alan Irvine begins his career as West Bromwich Albion manager at home to Sunderland, Tottenham Hotspur visit London rivals West Ham United, and Stoke City host Aston Villa.
Champions City travel to Newcastle United on Sunday, with Liverpool, the side they pipped to last season’s title, hosting Southampton. Chelsea, third last season, visit promoted Burnley on Monday.