After new United captain Wayne Rooney had cancelled out an opening goal from Ki Sung-yueng, Sigurdsson scored in the 72nd minute to hand United their first opening-day home defeat since 1972.
Wilfried Bony’s quick free-kick enabled Jefferson Montero to cross from the left and although Wayne Routledge miscued his volley, the unmarked Sigurdsson was able to finish from eight yards.
Manchester United's striker Wayne Rooney runs with the ball during the English Premier League football match between Manchester United and Swansea City at Old Trafford in Manchester, north west England. Pic/AFP
It was a goal that highlighted United’s defensive frailties, exacerbated by a lack of fit defenders that meant that winger Ashley Young had to be pressed into action at left-back in the second half.
Until that point, it appeared that former Netherlands manager Van Gaal was poised to prove himself the ideal successor to David Moyes, who was sacked in April after a dismal maiden campaign.
One of the main criticisms of Moyes’s reign concerned his tactical nous and it took Van Gaal only 45 minutes to suggest that he offers a serious upgrade in that department.
After an underwhelming first half, in which they trailed to Ki’s first goal for the Welsh club, Van Gaal brought on Nani to replace the ineffective Javier Hernandez.
Rooney operated as the spearhead of the attack, slightly ahead of Juan Mata, and it took the England forward just seven minutes of the second half to claim an equaliser, from Mata’s right-hand corner.
Phil Jones flicked the ball on from inside the six-yard box and Rooney struck with a clinical overhead kick from close range.
It was the first meaningful sight of goal for United, who had gone behind to Ki’s 28th-minute effort.
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Nathan Dyer cut in from the right before Sigurdsson helped the ball onto Ki, dead in front of goal on the edge of the area.
With Bony neatly -- and perhaps illegally -- blocking Jones’s attempt to close down Ki, the South Korean midfielder had time and space to plant a left-foot shot into the bottom-right corner.
At that point, it was hard to envisage how United would find a route back into the game, so inept had they been at turning possession into cutting-edge chances.
Wing-back Jesse Lingard, one of three debutants along with fellow academy product Tyler Blackett and new signing Ander Herrera, made a bright start but limped off midway through the first half with an injury sustained in a challenge with Ashley Williams.
That brought Adnan Januzaj, the Belgian winger, into the fray and his lack of defensive prowess would eventually force Van Gaal into his half-time tactical shift.
Before that switch, a mishit cross from Jones had been United’s only flutter of attacking excitement, although Swansea’s debutant goalkeeper Lukasz Fabianski tipped it over his crossbar easily enough.
The second half, and the equaliser, brought about an improvement from the home side, with Williams forced to make an excellent tackle following an equally impressive turn in the area by Rooney.
The same United man, suitably inspired by his new role, came up with a brilliantly executed 20-yard free-kick on 65 minutes that clipped the outside of the Swansea upright on its way behind.
But the second Swansea goal sucked any momentum out of United and Jones was required to make a superb tackle to deny substitute Bafetimbi Gomis.
When a United penalty appeal for a handball against Angel Rangel was waved away by referee Mike Dean in injury time, the hosts’ fate was sealed.
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