New-look Chelsea also suffered a reality check as British record signing Moises Caicedo's debut ended in a 3-1 defeat to West Ham.
By contrast, Pep Guardiola said Manchester City showed the mentality of champions to beat Newcastle 1-0 despite a demanding week that saw the treble winners add the UEFA Super Cup to their trophy haul.
AFP Sport looks at three talking points from the second weekend of the season:
New season, same problems for Man Utd
United got away with one on Monday as Wolves dominated at Old Trafford only to lose 1-0, in part thanks to the controversial non-award of a penalty to the visitors.
The performance from Erik ten Hag's men was marginally better at the Tottenham Hotspur Stadium, but against stronger opposition this time their failings at both ends of the field were punished.
Ten Hag admitted he is concerned by his side's inability to make the most of their chances after a number of gilt-edged first-half opportunities went begging.
The Dutchman said that is the reason United splashed out £64 million ($81 million) on Danish striker Rasmus Hojlund.
But the 20-year-old has missed the start of the season due to a back injury, exposing United's need for a natural number nine once more.
Marcus Rashford's desire to start from the left rather than through the middle shone through, while Ten Hag needs more end product from wingers Antony, Alejandro Garnacho and Jadon Sancho.
No Caicedo, no problem for Brighton
Just days after Brighton raked in a record transfer fee rising to £115 million for Caicedo, they still ended the weekend top of the table.
Roberto De Zerbi's men backed up their 4-1 win over Luton on the opening weekend by thrashing Wolves by the same scoreline at Molineux.
The Italian has said bigger clubs may buy Brighton's best players but not their spirit.
Caicedo, who joined the Seagulls for just £4 million just two years ago, has cost Chelsea more than Brighton spent to build their Amex Stadium.
The Premier League's vultures are likely to be hovering once more for Kaoru Mitoma in the near future.
The Japanese winger shone last season and opened the scoring in stunning fashion as he slalomed past four Wolves defenders before slotting home.
Mitoma then set up the second goal for Pervis Estupinan before Solly March struck twice.
City show Newcastle gulf still to bridge
Backed by the vast riches of the Saudi sovereign wealth fund, Newcastle appear best placed to challenge City's dominance of English football in the coming years.
The Magpies headed to the Etihad full of confidence after thrashing Aston Villa 5-1 to get their season off to a flying start.
But Newcastle were given a reminder of the gulf in class they still have to bridge if they are to take City's crown and become English champions for the first time in 97 years.
Pep Guardiola's men arrived home in the early hours of Thursday morning after edging out Sevilla on penalties in punishing conditions under baking heat in Athens.
The City boss was furious at the scheduling of the game, but hailed his players' mentality to rise to the challenge.
Julian Alvarez scored the only goal with a terrific strike into the top corner.
City controlled the game throughout and could have won more comfortably but for a rare off night in front of goal for Erling Haaland.
"The difference with this group is the mentality for many, many years," said Guardiola.
"Last year they did it and in the second game today they have done it. Nothing changes."
