The Wales international midfielder emphatically fired home the only goal of the match at Turf Moor after 12 minutes.
Arsenal's winning streak is the best recorded by any Premier League team this season, while it includes four victories away from home and three clean sheets.
It leaves them four points behind Premier League leaders Chelsea having played two games more.
Ramsey acknowledges that the swashbuckling style synonymous with Arsene Wenger's sides has not always produced such results, and he was pleased to avoid a slip-up against a team many of the league's leading lights have struggled against this term.
"A lot of big teams have dropped points here this season," he told Sky Sports after marking his 150th Premier League appearance in style.
“It was another difficult game and another test that we got through.
"I think we looked pretty solid. They like to get the ball forward and cross the ball into the box but I felt we dealt with it ever so well.
"Maybe in the past we've been a bit guilty of trying to go forward and then being punished in the latter stages of the game.
"But I thought we controlled the game pretty well. We were under pressure but we felt pretty comfortable out there defending.
"It's another win and another win away from home."
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