Wenger had looked set for a 65th birthday to forget when his side trailed to a second-half header from Andy Najar going into the closing stages of the Group D clash at the Constant Vanden Stock Stadium.
Former Portsmouth defender Anthony Vanden Borre had a miskicked effort loop onto the top of the crossbar, before third-choice Arsenal goalkeeper Emiliano Martinez saved from Steven Defour as Anderlecht looked to seal a famous victory.
However, a superb volley from left-back Kieran Gibbs levelled the tie on 89 minutes, before substitute Lukas Podolski swept home an unexpected winner.
"We played against an Anderlecht team that were well organised, very focused, very quick in the transition and very good in the challenges," Wenger said.
"The turning point was not to concede the second goal
They had a good chance that they didn't take and, in the end, the quality of our players who came on and our experience made the difference.
"But as long as we didn't concede the second goal, I thought we had a chance to take at least a point.
"It us a bit unexpected to take the three, considering the quality of the match that Anderlecht played tonight."
Wenger added: "I know by experience that the last five minutes in the Champions League, the nerves play a part, and that we had to get into these five minutes without conceding the second goal.
"Of course, if they had scored the second goal, it was game over.
"I had hope
It didn't look like (it would happen), but it happened and that means we took all the risks and, in the end, it paid off.
"It is a little bit a gambling situation that happens in this kind of games and it worked tonight.
"But it did not look obvious, that is for sure."
Germany forward Podolski has seen his first-team chances limited this season, but Wenger retains full faith in the World Cup winner, who had been linked with a move away from the Gunners.
"He is frustrated and I understand that of course, but he is important as well and he showed that tonight and he will be important in the coming months," Wenger said.
"It took him a while to get back to a good physical level [after the World Cup] and now he is nearly there.
"He was never close to leaving
He has more than one hundred caps for Germany that is not a coincidence, and shows you his quality.
"Podolski is a guy you want to have the ball in the box because his shot is fantastic and his accuracy is great."
Arsenal had lost their opening Group D match away to Borussia Dortmund, but, with two home ties coming up, against Anderlecht and then the German side, the Barclays Premier League side still hold qualification very much in their own hands.
"We have learned a lot about Anderlecht tonight and if we beat them (again) then we have a good chance to qualify
After we play Dortmund at home and will see what we can do," Wenger said.
Anderlecht coach Besnik Hasi, meanwhile, was left less than impressed by the way his side were defeated.
Hasi claimed there had been a clear foul on Defour in the build-up to Arsenal's winner, which was not given by Spanish referee Carlos Velasco Carballo.
"The performance of my team was nearly perfect, apart from in the last three minutes," he said.
"We should have won this game
Arsenal were never in it until the end.
"We tried to score the second goal, but when you don't they can catch you.
"We really missed the focus on ourselves after they had equalised and it is the second time (in the Champions League this season) we have lost points this way.
"But there was a huge foul (on Defour) and the referee has to take responsibility for that, but this is what happens with a smaller club sometimes."
Source : PA
Source: PA