Alexandre Lacazette will get the glory following his brace, but West Brom had a strong call for a penalty turned down by referee Bobby Madley in the eighth minute when Shkodran Mustafi brought down Jay Rodriguez in the box.
After the match, Ramsey told BBC Sport: "We know all about their team. They are very organised but our application was good tonight.
"Alexandre Lacazette has made a fantastic start. He is a fantastic player and we are lucky to have him. We want to make this a fortress and we have three wins here now. Hopefully that can continue."
On West Brom's penalty appeal, the midfielder added: "I was far up the pitch so I am not sure but there are hundreds of decisions referees have to make in a game. I think he had a solid game."
Arsenal are currently seventh in the league table.