Santi Cazorla struck five minutes from time to give Arsenal a morale-boosting 2-1 over a plucky Aston Villa side.
Pundits and some sections of the Arsenal support had begun to question Wenger over the previous seven days following Arsenal's FA Cup exit to Blackburn and their 3-1 home defeat to Bayern Munich in the Champions League.
Although the performance in north London was hardly vintage Arsenal, the win moves Wenger's men to within one point of Tottenham, who play their game in hand on Monday night at West Ham.
And with a crunch north London derby coming up at White Hart Lane next weekend, Wenger hopes the turbulent past week will now be nothing but a distant memory.
"I hope this gives us a bit more quietness for us to prepare our next game. It was a very important day for Arsenal Football Club," the Arsenal manager said. "I am very happy for the players because they have a good attitude and want to do well.
"We went through some difficult times so it was important first to show that we are united, determined, and focused to win the game, and we were.
"We were a bit nervous - I concede that - because we are under a lot of pressure, we had our backs to the wall and had to win the game."
The way Arsenal surrendered their only realistic hope of silverware against Championship side Blackburn, and the way they were completely outclassed by Bayern, were signs to some that Wenger's powers were on the wane.
A bizarre press conference rant prior to the game against last year's Champions League finalists also gave ammunition to Wenger's critics.
The Frenchman insisted later in the week that he had never contemplated quitting the club he joined 17 years ago, but he admitted yesterday that the past seven days had been tough.
"Honestly, I have been well-tested (over the last week)," the 63-year-old said.
"It is not the critics that have been tough. I'm not masochistic - I prefer that (the media) say I'm good rather than bad, but I can understand that is part of my job.
"What was very, very difficult to take was to lose against Blackburn in the FA Cup at home and after against Bayern, it can go both ways - but one after the other, to lose big games, that is what was absolutely terrible.
"We question ourselves always as coaches. You are not 30 years in your job if you don't question yourself. It is a bit more challenging now. I don't think it is down to the methods of coaching or training or managing the team. Opinions are multiplied by a thousand - everyone knows exactly what you should do, but not everybody has been on a football pitch."
Cazorla swept home after five minutes after seeing his initial attempt blocked, but Andreas Weimann stunned the home crowd 22 minutes from the end with a brilliant equaliser on the counter.
The impressive Austrian switched off with five minutes to go, though, allowing Nacho Monreal space to cross for Cazorla, who fired home the winner from close range.
The result means Villa drop back in to the relegation zone, but manager Paul Lambert is confident his team will not go down.
"If they're playing like that they will believe they can stay up, I do," the Scot said.
"I had no qualms with them at all. They've been fairly criticised in some quarters, but they've never let their heads go down. They've always responded. And we shouldn't have lost that game."
Lambert's situation has not been helped by injuries to key players like captain Ron Vlaar, however, who missed yesterday's game.
"He's got a problem with his calf," Lambert added.
"Hopefully it won't be long-term."