Viktor Gyokeres scored twice to open his Gunners account while defender Jurrien Timber also notched a double.
But Arsenal manager Mikel Arteta said the injuries to key players Saka and Odegaard, just days after Kai Havertz was also ruled out by a knee injury, showed why he needs such a deep squad.
“We’ve learned the lesson from last season and the squad that you need right now,” said Arteta.
“That is why we acted in the market the way that we have done because you have so many games, anything can happen.
“It happened to two of our most important players - we already lost Kai - so we are going to need everybody at his best and a lot of luck as well to not lose others.”
A new-look Manchester City were left stunned at the Etihad as Tottenham strolled to a 2-0 win, Brennan Johnson and Joao Palhinha striking for the Europa League winners just before half-time to continue the perfect start for Thomas Frank after two league games in charge.
City’s run of four consecutive Premier League titles came to a spectacular end last season as they finished a distant third behind Liverpool and Arsenal.
A 4-0 thrashing of Wolves on the opening weekend of the campaign showed glimpses of a revamped City back to their best.
However, they were again easily exposed on the counter-attack, while manager Pep Guardiola must decide who will be his number one goalkeeper after a day to forget for James Trafford.
Ederson was left on the bench amid rumours the Brazilian could join Galatasaray before the transfer window closes. City have been linked with a move for out-of-favour Paris Saint-Germain ‘keeper Gianluigi Donnarumma.
Tottenham took the lead on 35 minutes when Richarlison squared for Johnson to power past Trafford.
The England goalkeeper then had a moment of madness when he attempted a pass to Nico Gonzalez inside his own box.
Pape Matar Sarr intercepted and, even though the goalkeeper recovered to deny Richarlison, Palhinha smashed home the rebound.
Spurs let a two-goal lead slip late on against PSG to lose the UEFA Super Cup in Frank’s first game in charge earlier this month, but rarely looked in danger of suffering a similar fate.
“From every game you learn and games where you don’t get the result you learn even more,” said Frank.
“Defensive principles and the mentality is the key thing. We need this mentality to win games like this.”
Hammers Hammered
Chelsea came from behind to thrash West Ham 5-1 on Friday and leave former Blues boss Graham Potter under pressure just two games into the season.
Potter has won just five of 21 games since taking charge in January and has endured a miserable start to the new campaign after a 3-0 defeat to newly-promoted Sunderland the previous weekend.
Joao Pedro, Pedro Neto, Enzo Fernandez, Moises Caicedo and Trevoh Chalobah were all on target for Chelsea while Lucas Paqueta scored the consolation for the Hammers.
Aston Villa have failed to score in their opening two games after losing 1-0 at Brentford, while Marcus Tavernier scored the only goal as Bournemouth beat 10-man Wolves 1-0 and Burnley secured their first points back in the top flight with a 2-0 win over Sunderland.
The Black Cats beat West Ham 3-0 last weekend on their return to the Premier League after an eight-year absence but goals from Josh Cullen and Jaidon Anthony brought Sunderland back to earth.
In yesterday’s games, Crystal Palace and Nottingham Forest drew 1-1, as did Fulham and Manchester United, while Everton christened their new stadium with a 2-0 win over Brighton.
Newcastle United host defending league champions Liverpool this evening, a game given extra spice due to the ongoing transfer drama between the clubs involving Toon striker Alexander Isak.