Only Manchester City and Brighton had won their opening two games but the Gunners joined them on six points after a narrow success at Selhurst Park.

In a close-fought encounter, captain Odegaard stepped up to steer home a second-half spot-kick, with the visitor then hanging on for the final quarter of the game after Takehiro Tomiyasu was sent off.

The defender was the only change to Mikel Arteta’s starting XI from their opening-day win against Nottingham Forest as he replaced the injured Jurrien Timber at left-back – but he will now be banned for Saturday’s visit of Fulham after a controversial dismissal here.

Palace – unchanged from its win victory at Sheffield United a week ago – was fast out of the blocks, Aaron Ramsdale making a low stop to keep out an Eberechi Eze drive as the host built up a head of steam.

Cheick Doucoure then flashed a speculative effort wide as Arsenal struggled to get a foothold on proceedings.

The visitor gradually started to see more of the ball and Eddie Nketiah was unfortunate to see his shot come back off a post after beating Sam Johnstone in the Palace goal.

With the game opening up, both sides had good chances, with Jordan Ayew almost capitalising on a poor William Saliba touch, only for the France defender to makes amends with a fine, last-ditch tackle.

Arsenal went down the other end and Nketiah wasted a gilt-edged opportunity as he tried – and failed – to execute a deft lob over Johnstone from close range.

Odegaard was next to come close to breaking the deadlock for Arteta’s side, his curled strike from outside the box tipped over by Johnstone.

Arsenal would eventually hit the front soon after the restart, Gabriel Martinelli’s quick free-kick playing in Nketiah, who went to ground under pressure from the sliding Johnstone.

Referee David Coote pointed to the spot and the decision survived a VAR check for a foul by Thomas Partey in the build-up, with Odegaard making no mistake as he sent Johnstone the wrong way from 12 yards.

Coote was to make another couple of controversial calls shortly after, showing a yellow card to Tomiyasu for time-wasting at a throw-in before dismissing the Japan full-back seven minutes later for a soft foul on Ayew.

Arteta reacted by introducing Gabriel Magalhaes in place of Martinelli, while Jorginho replaced Nketiah as Arsenal shut up shop in the closing stages.

Jakub Kiwior and fit-again Oleksandr Zinchenko added even more steel to the defensive unit as Odegaard and Bukayo Saka made way.

It proved just enough to keep Palace at bay, the Arsenal rearguard high-fiving and celebrating every challenge and clearance as they hung on to secure the win.