Swansea City condemned Louis van Gaal to defeat in his first Premier League game as Manchester United manager on Saturday, while Aaron Ramsey scored a stoppage-time winner for Arsenal.Van Gaal was taking charge of his first competitive match at United, but his new side exhibited many of the same failings from last season - when they finished seventh - as they slumped to a 2-1 loss.
"It is very disappointing that we have lost our first home match," said Van Gaal, who handed competitive debuts to 20-year-old Tyler Blackett and 21-year-old Jesse Lingard.
"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."
Gylfi Sigurdsson, back at Swansea after two years at Tottenham Hotspur, gave his side victory by squeezing a shot past United goalkeeper David de Gea in the 72nd minute after Wayne Routledge miscued a volley.
Sigurdsson had earlier teed up South Korea midfielder Ki Sung-yueng to stroke home a 28th-minute opener, before new United captain Wayne Rooney hooked in an equaliser for the injury-ravaged hosts.
"We have been working hard in pre-season on defensive shape and we can get even better at that," Swansea manager Garry Monk told BT Sport.
"But there were pleasing signs in the way we stuck together and the goals we scored against a side of Manchester United's resources."FA Cup winners Arsenal opened their campaign with victory after Ramsey gave them a last-gasp 2-1 success at home to Crystal Palace, who are without a manager following Tony Pulis's shock departure on Friday.
Laurent Koscielny was caught napping by Hangeland's dart to the near post, but the Arsenal centre-back atoned in first-half injury time by ghosting in to head home a teasing free-kick from Sanchez.
Palace had Jason Puncheon sent off for two bookable offences and Arsenal capitalised in the 91st minute when Ramsey notched from close range after Julian Speroni had saved from Mathieu Debuchy.
Dier's dream debut
"Credit to Palace, they fought hard. They were physically very strong, very organised," Arsenal manager Arsene Wenger told Sky Sports. "We keep going. That's one of our strengths and it paid off today."
On Ramsey, Wenger added: "He has something that is a real gift, to be where you need to be in the box."
The late excitement at the Emirates Stadium was mirrored in three other games.
New Zealand striker Chris Wood came off the bench to earn promoted Leicester City a dramatic 2-2 draw at home to Everton in their first top-flight game since 2004.
After Leicester new recruit Leonardo Ulloa had cancelled out Aiden McGeady's precise 20th-minute opener, Steven Naismith looked to have given Everton victory, only for Wood to fire home four minutes from time.
Eric Dier enjoyed a dream debut for Tottenham by scoring a 93rd-minute winner at West Ham United in manager Mauricio Pochettino's first game at the Spurs helm.
After Tottenham full-back Kyle Naughton and West Ham centre-back James Collins had both been sent off, substitute Dier coolly rounded goalkeeper Adrian in stoppage time before rolling home the game's only goal.
"I am not sure why I was up in attack, to be honest," said Dier, a 20-year-old English centre-back who signed from Sporting Lisbon two weeks ago.
"I'm told the assistant boss said to the manager, 'What's he doing there?' And even I don't know why I was there. I don't normally get into those positions."
At The Hawthorns, meanwhile, new West Bromwich Albion manager Alan Irvine was denied victory against Sunderland by an 85th-minute goal from Sebastian Larsson.
West Brom led 2-1 after Saido Berahino replied to Lee Cattermole's early 25-yard strike with a brace, but Larsson earned Sunderland a 2-2 draw by sweeping home a cut-back from debutant Patrick van Aanholt.
Elsewhere, James Chester's 52nd-minute header gave Hull City a 1-0 win at promoted Queens Park Rangers, while Andreas Weimann earned Aston Villa a 1-0 victory at Stoke City.
Champions Manchester 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.