Matt Jarvis' 40th-minute header put the visitors ahead at the Emirates Stadium on Tuesday but two strikes from Lukas Podolski and a sublime goal from Olivier Giroud boosted Arsenal's UEFA Champions League qualification hopes.
At times during the first half, Arsenal showed signs of tiredness after Saturday's penalty shootout FA Cup semi-final victory over Wigan Athletic, but Wenger's men rarely looked like losing after drawing level in the contest.
Podolski's first goal cancelled out Jarvis' brave header just before the break and Wenger labelled the German's goal as the turning point in the game.
"I think we built the victory tonight through consistency in our game," he told Sky Sports. "The first half it was difficult but the vital thing was to comeback right before half time.
"In the second half we controlled the game.
"Overall it is a hard fought win but a very, very important one, and a pleasant one because after Saturday's game we had to dig deep.
"It was two compulsory wins, we did it, let's continue like that.
"Everybody's under pressure to do well, and the best way to deal with that pressure is to focus on your own performance."
Podolski was given only his 10th start in the Premier League this season and he rewarded Wenger's faith with a goal in either half on Tuesday.
However, it was the first-time control and finish from Giroud for Arsenal's second goal that impressed Wenger the most.
"It was a great goal," he added. "First touch with his left foot and finishes well with his right foot, credit to Thomas Vermaelen who gave him a great ball but there was a lot to do after that.
"(It was) a fantastic goal.
"If the first touch in the box is not perfect you do not have a chance to score, that touch was perfect."
