Arsenal had failed to win any of their previous three league games but took the lead after 23 minutes on Saturday through an Ozil volley from just inside the area.
Subsequent chances to put the game away were wasted, leading to a nervy conclusion to the 1-0 triumph as Newcastle spurned opportunities to level.
Wenger admitted it could have been a bigger win, but was happy to see Ozil play the pivotal role with a great strike.
"We have created the chances to be comfortable and in the last five minutes we became a bit edgy.
"We didn't make a mistake at the back, you could see that necessity to win was playing a bit on the mind of our players in the end and the fact as well that we could not take our chances, you try to force it too much and to not play with enough freedom.
"[The goal] was a gem to watch. I'm happy for Mesut because that's what you want from him and he took it with decisiveness. It was a fantastic goal."
This win is dedicated to the many young guests at #AFCvNUFC charity matchday. Three icecold points remain at the Emirates today. Thanks for the support, Gooners. @Arsenal #YaGunnersYa pic.twitter.com/sxhgXbKWkl — Mesut Özil (@MesutOzil1088) December 16, 2017
Rafael Benitez's Newcastle have now taken just one point from their last nine games, leaving them in the relegation zone - a point adrift of safety.
Benitez said: "We had our chances. We were pushing and attacking. We had chances to draw. It's a pity. We are learning. In some games we are one goal behind. The players are working hard.
"We knew this could be difficult. Two or three games we could draw or win. We need to be competitive like today and keep going. We are a young team. When you're not winning you lose confidence.
"We have to keep working this way. Try to get a result. In January, try to bring in people.
"The fans know the team will be tough. They also know we need something in January - that will help the current squad."