Arsenal shrugged off Takehiro Tomiyasu's red card to extend their perfect start to the Premier League season as Martin Odegaard sealed a 1-0 victory against Crystal Palace on Monday.
Odegaard's second-half penalty at Selhurst Park put Arsenal on course for their second successive win.
But Mikel Arteta's side had to dig deep to preserve the points after Japan defender Tomiyasu was controversially sent off for a second yellow card midway through the second half.
Tomiyasu had been booked for taking too long over a throw-in before his dismissal for making minimal contact on Jordan Ayew.
Arteta was delighted with the way Arsenal refused to surrender their lead as they moved up to third place, behind leaders Brighton and second-placed Manchester City on goal difference.
"Great win. I'm so happy. To play 30 minutes away from home with 10 men is extremely difficult," Arteta said.
"Some players were suffering physically. The subs were magnificent, they knew what they had to do.
"Today we had a difficult one, we overcame it and it will make us better."
Frustrated by Tomiyasu's first booking for time-wasting, Arteta added: "This is the standard. I think it was eight seconds. We might have to play with a stop watch."
Expected to mount a sustained title challenge following last season's late collapse that gifted the trophy to City, the north Londoners look up for the fight after building on their opening weekend win against Nottingham Forest.
While they haven't played their most fluent football yet, this could prove a significant building block in their bid for a first title since 2004.
Arsenal had the best away record in the top flight last season and registered a division-best 10 clean sheets on their travels.
Arteta's men looked like road warriors again as they repelled Palace's late flurry of pressure.
With new goalkeeper David Raya among the Arsenal substitutes after his loan move from Brentford, the spotlight was on Aaron Ramsdale as the England international fights to hold onto his place.
Ramsdale rose to the challenge with a confident display from the moment he turned away Eberechi Eze's long-range strike in the early stages.
ICE-COOL ODEGAARD
Emulating City boss Pep Guardiola's tactic of instructing a defender to advance forward whenever they have possession, Arteta deployed Thomas Partey at right-back with a license to link up play from his preferred midfield role.
That allowed Arsenal to dominate possession but Eddie Nketiah, deputising for the injured Gabriel Jesus, failed to make their first-half pressure pay off.
The 24-year-old wasted a good chance when he nimbly turned away Joachim Andersen, only to scuff his shot against the far post with just Sam Johnstone to beat.
Palace were denied a penalty after William Saliba's sliding tackle on Ayew was ignored by VAR.
Nketiah was profligate again when he chipped over from just six yards after Declan Rice picked out the unmarked forward.
Arsenal kept their composure and Odegaard's fierce 25-yard strike forced a superb tip over from Johnstone.
Odegaard wouldn't be denied again as the Norwegian netted from the spot in the 54th minute to reward Arsenal's dominant display.
Gabriel Martinelli's quick free-kick caught Palace dozing and Nketiah rounded Johnstone before being upended by the keeper, who was sent the wrong way by Odegaard's ice-cool penalty.
When Partey's blast from the edge of the area was slapped over by Johnstone, it looked like Arsenal would cruise to victory.
But Palace were given a glimmer of hope in the 67th minute as Tomiyasu was harshly dismissed for a slight push on Ayew that was not reviewed by VAR under rules governing second yellow cards.
Palace's frustration mounted when Eze went down under contact from Partey but saw his penalty claim rejected.
In a tense finale, Odsonne Edouard had Palace's best chance to equalise when he headed wide from Tyrick Mitchell's cross.
Mitchell also squandered an opportunity, blazing over from six yards as Arsenal held firm.