Swansea City condemned Louis van Gaal to defeat in his first English Premier League game as Manchester United manager yesterday, while Aaron Ramsey scored a stoppage-time winner for Arsenal.
It was van Gaal's first competitive match at United, but his new side retained many failings from last season - when they finished seventh - as they slumped to a 2-1 loss.
It was Swansea's second consecutive win at Old Trafford, after an FA Cup third-round success in January, and dealt United their first home defeat on opening day since 1972.
"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 ... 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.
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 after Welshman Tony Pulis' shock departure on Saturday.
New signing Brede Hangeland gave Palace a 35th-minute lead, shrugging off Arsenal star signing Alexis Sanchez to meet Jason Puncheon's in-swinging corner with a glancing header.
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 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.
"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."
In other matches, 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 Spurs fullback 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, 20, 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, 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 23-metre strike with a brace, but Larsson earned Sunderland a 2-2 draw by sweeping home a cut-back from debutant Patrick van Aanholt.
James Chester's 52nd-minute header gave Hull City a 1-0 win at promoted Queens Park Rangers, and Andreas Weimann earned Aston Villa a 1-0 victory at Stoke City.
Arsenal 2 Crystal Palace 1
Leicester City 2 Everton 2
QPR 0 Hull City 1
Stoke City 0 Aston Villa 1
West Brom Albion 2 Sunderland 2
West Ham 0 Tottenham Hotspur 1
Manchester United 1 Swansea 2