Arsene Wenger has praised Sam Allardyce's "well organised" Sunderland side after pushing the Gunners all the way.
The Arsenal boss was a relieved man at the final whistle after seeing his side end a run of three Premier League games without a win.
Victory elevated the Gunners to second in the table.
But it was a far from comfortable afternoon at a blustery Emirates Stadium, with Sunderland going toe-to-toe with title-chasing Arsenal.
Wenger admitted afterwards he had been more nervous than usual before the game, as he knew the importance of getting three points against Sunderland.
And he was impressed with the display by Allardyce's men.
Wenger said: "We were edgy and nervy in the first half against a very well organised team, who were very impressive on the counter-attack as well.
"But in the second half we showed mental strength and desire and more incisiveness in our game.
"And more fluency as well. Even if all was not perfect, the team has shown mental strength.
"We scored an own goal just before half-time, the worst that can happen to you, but we still managed to win the game.
"If you rush forward, there were dangers with [Steven] Fletcher and [Duncan] Watmore and their full-backs too, who could have exposed us.
"It was important for us not to concede the second goal, and to play a bit more behind their midfield - behind Ola Toivonen and Yann M'Vila, to find space behind their centre backs."
Sunderland fell behind to a Joel Campbell strike before an Olivier Giroud own goal from an M'Vila free-kick on the stroke of half-time saw the Black Cats draw level.
Second half goals from Giroud and a stoppage time third from Aaron Ramsey sealed the win.
Wenger added: "I was more nervous than usual because I felt it was a very important game for our season.
"I knew that Sunderland would be good on the counter attack and on free-kicks.
"We played not to give many free-kicks away and they played to get free-kicks.
"They did that well.
"I wasn't happy with the free-kick awarded [that led to Sunderland's equaliser] but I have been told since that I was wrong, so I accept it!"
Wenger was satisfied to end a run of three Premier League games without a win as Arsenal moved up to second in the table.
And he praised his side's response to conceding the unfortunate equaliser on the stroke of half-time..
"It was a very important game for us because we came out of three disappointing results," he said.
"We had lost only one game but I think it was a very, very important game for us, psychologically, for the fact we had not won, for the fact we had lost important players in our side and we had to show that we can win."