Arsenal captain Martin Odegaard's penalty secured a 1-0 win over Crystal Palace after the visitors finished with 10 men following Takehiro Tomiyasu's sending off for two yellow cards in their Premier League clash at Selhurst Park on Monday.

Both sides had a number of decent chances in the first half-hour with the best of them falling to Arsenal's Eddie Nketiah, who hit the post in the 29th minute after some good pressing by the midfield saw the Gunners win the ball high up the pitch.

- Stream on ESPN+: LaLiga, Bundesliga, more (U.S.)

Nketiah wasted another great chance in the 36th after he was played in behind the defence by Declan Rice as he fluffed his attempted chip which flew harmlessly over the crossbar.

The striker was in the thick of things again early in the second half as he was felled in the box by keeper Sam Johnstone when running onto a quick free kick by Gabriel Martinelli.

Referee David Coote pointed to the spot and Odegaard sent Johnstone the wrong way, rolling the ball in at the foot of the keeper's right-hand post.

Arsenal looked set to cruise to victory but Tomiyasu was shown his first yellow card on the hour mark for time-wasting at a throw-in and was sent off in the 67th minute when he collected his second booking for a foul on Jordan Ayew.

Arteta quickly made a number of defensive substitutions that caused problems for Palace and the closest the home side came to an equaliser was a stoppage-time snap-shot by fullback Tyrick Mitchell that flew wide.

The win lifted Arsenal to third on six points behind Brighton & Hove Albion and Manchester City on goal difference. Palace have three points from their opening two games.

"If you want to win the Premier League, if you want to be up there at the end of the season, these are the stadiums you've got to come to show character," Arsenal midfielder Declan Rice told Sky Sports.

Palace defender Joel Ward was disappointed with the defensive lapse that saw his side suffer defeat after an opening day win at Sheffield United.

"I think we definitely deserved something out of the game, the way we played as a unit today. We went toe to toe with them and it was one moment that maybe caught us off guard," he said.

"It is one of those - sometimes you get them and sometimes you don't and this time it went against us," he added.