Summer signing Ozil showed a delightful first touch before setting up Olivier Giroud, who gave Arsenal the lead in the 11th minute at the Stadium of Light.
However, the Black Cats fought back and Craig Gardner equalised from the penalty spot three minutes after the break following Laurent Koscielny’s foul on Adam Johnson.
But Ramsey netted twice in the last 35 minutes to hand the Gunners their fifth straight win in all competitions.
“You’ve seen what he is all about slipping those balls in, he has one of highest assist-rates in Europe and he is going to create a lot of opportunities for us,” said Ramsey before expressing his delight at netting the Gunners’ second and third goals.
“I’m delighted to be on the scoresheet again. In the last few seasons I’ve been getting into right positions but maybe I’ve been lacking a bit of composure but I’m enjoying it now.”
There was controversy moments after Ramsey’s first strike when Sunderland forward Jozy Altidore was denied a goal as referee Martin Atkinson failed to play an advantage.
And Gunners boss Wenger admits his side were fortunate that the goal was not awarded.
“We were a bit lucky at 2-1 maybe, but we found the mental resources to win,” said Wenger, whose side moved top of the Premier League table.
“It could have been a foul for us as well because Altidore took Sagna as well but the referee blew before the goal, I was sure of that because I saw him.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news