Sterling, who was City's captain on the evening, settled the game in the first half with a confident finish with his weaker left foot.
Riyad Mahrez picked out Sergio Aguero expertly, and the returning Argentine played in Foden, whose shot was parried by Leno straight into the path of Sterling, who calmly finished into the bottom corner.
The skipper, who operated quite centrally against the Gunners, admitted that he could have done more, but was grateful to be the one to decide the result.
"It was not one of my better games but I am just grateful to be able to help the team," he said. "At times in the first half, me and Sergio [Aguero] got on the ball really well in the pockets in front of their defence and took up some great positions.
"It felt like we were much more fluent and able to keep possession. To have a striker to link up with was really good.
"It's one of them positions about being in the right place and it was perfect for me because I was there to tuck it away."
After defeat to Leicester last time out at the Etihad, and then drawing against Leeds in our last league encounter, Sterling stressed the importance of getting back to winning ways.
"We dropped points early on in the season so it was important to keep on winning.
"Coming back from the international break we knew we needed a good performance and to pick up points to kick-start the season. Today's result definitely gives us confidence."
The winger also showed his appreciation to the visitors, managed by former City assistant boss Mikel Arteta.
"They closed the pitch well and they had some good chances as well," he admitted. "It was a tough team to play against and Mikel has them well drilled."