Arsenal struggled for large periods against the Belgian side and looked to be heading for their second defeat in Group D after another stagnant Champions League performance.
But Wenger's sleight of hand in the closing stages ensured Arsenal finished with six attack-minded players on the field and it worked wonders as Kieran Gibbs and substitute Lukas Podolski scored in the final two minutes to snatch a 2-1 victory.
"We took all the risks and, in the end, it paid off," Wenger, whose side are second with six points from three matches, told reporters afterwards.
"It's a little bit of a gambling situation that happens in this kind of game and it worked. It did not look obvious, that is for sure.
"In the end, the quality of the players who came on and our experience made the difference, unexpectedly."
Arsenal, who have won just two of eight games in the Premier League this season, have struggled to play with the elegance for which they are renowned in recent weeks and the performance against Anderlecht added to Wenger's frustrations.
"We had the spirit but it was disappointing that we didn't create more," the Frenchman said. "I put that down to the fact that Anderlecht defended very well.
"It's a bit unexpected to take the three points, considering the quality of the match that Anderlecht played.
The Belgian side were just minutes away from ending a run of five successive home defeats in the group stage of the competition before Arsenal left them ruing their missed chances which would have sealed the win.
"We controlled the game in the first half without creating any chances. In the second half, we opened ourselves up and were a bit more vulnerable on the counter-attacks," Wenger admitted.
Midfielder Jack Wilshere was also relieved to escape from Brussels with three points after admitting Arsenal are far from their best at the moment.
"Maybe we didn't put in the performance here, but we got the result - and we'd much rather have it that way," Wilshere told the club's website.
"It wasn't our prettiest performance, but we won the game and that's all that matters.
"We've been through a bit of a rough stage where we haven't been winning games, so the main thing was to get the three points."
(Editing by Mike Collett)
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