The Spanish playmaker and the German forward both netted their first goals for the Gunners to help the visitors to an impressive three points.
Wenger is thrilled that his new recruits have made their mark early and says he is convinced all the summer signings he made will prove to supporters they can replace the top stars who have left the Emirates Stadium in recent years.
"Of course it is good when new signings start well and score a goal," he said.
"Arsenal is a club that has had many great players, so the new signings have to convince people that they can follow and be the same.
"I'm sure that in time these new players we have brought in will prove to the fans that they have the ability to play for us.
"Everyone understood Cazorla would not need six months to settle in - I am pleased for him. For the first goal it was good to get Podolski in with a chance on his strong left foot.
"It is a very encouraging start, we have played two away games now at difficult places - Stoke and Liverpool - so overall I have to be happy.
"We put in a terrific performance. At the start of the season we didn't have very good cohesion and we lacked a bit of sharpness. That gets better from game to game and it improved again here."
While the Frenchman was happy with the fluid attacking play on show at times from Arsenal, he was most pleased with a third consecutive clean sheet.
"Overall we were solid in our usual passing game and scored two good goals but we were also very good defensively," said Wenger.
"Our defending was good again. It's like scoring goals - you go on a run. As long as you don't concede you keep playing better as you want to keep the record going. We are defending well as a team.
"I don't know if we are a stronger team than we were last season yet. Last year we went through a difficult start, we had to buy four or five players on deadline day so we were a bit less serene than we are now.
"Unfortunately we have lost Robin van Persie over the summer but we couldn't do anything about that."