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."