Ramsey has started the season in terrific form and he was impressive again as he helped the Gunners to victory at the Stadium of Light.
He has worked hard on his finishing and believes he is beginning to reap the rewards, although he admits Arsenal made hard work of seeing off the Black Cats.
"We were totally in control in the first half and then we conceded a goal very early in the second half," the Welshman told Sky Sports.
"The crowd were right behind them and we were under pressure, but we had to dig in and be patient and the goals came at the end. And I thought we deserved it in the end.
"I am delighted to be on the score sheet again. I feel like in the last few seasons I have been getting in the right positions but I've lacked composure maybe.
"Now I am feeling good again and everything is starting to click into place."
Ramsey is also relishing the prospect of lining up alongside Mesut Ozil on a weekly basis after the German impressed on his Arsenal debut.
"Absolutely. You have seen what he is all about today. He is a fantastic player and I think he is going to create a lot of opportunities for us," said Ramsey.