After a goalless first half, the Belgian side took the lead in the 71st minute when Honduras winger Andy Najar headed in Dennis Praet’s cross.
Anderlecht missed a number of chances to double their lead before Kieran Gibbs volleyed home Calum Chambers’ brilliant cross to level in the 89th minute.
And substitute Podolski completed the comeback when he fired home from close range a minute later to keep Arsenal second in their group.
“We looked to control the game in the first half and control their counter-attacks as well but slowly in the second half we opened ourselves up,” Wenger told Sky Sports.
“Defensively we got caught. After that, the crucial point was when we were 1-0 down they don’t take their chances to score the second goal.
“We kept going and managed to score two good goals, because we had the spirit. But Anderlecht played well tonight and you can see this country produces top-class players.
“It was a vital win for us to have a chance to qualify. We are in a strong position now. Galatasaray and Anderlecht have only one point and we have six, Dortmund nine. It’s down to us now to win our home games.”
Wenger concluded: “We fought until the last second and we know from experience that in the Champions League many goals are scored in the last five minutes and we took advantage of that.”
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