The 23-year-old's sensational 30-yard half-volley, crashing the ball back into the top corner after it was cleared from a corner, was applauded by the home fans, despite seeing their side fall 3-0 behind, and sparked debates about great goals on social media.
Arsenal had made an electric start on Tuesday night at the Turk Telekom Arena, which had plenty of empty seats after Galatasaray's forgettable Champions League Group D campaign, with a goal from Lukas Podolski after just two minutes, the German forward making the most of a rare opportunity in the first XI.
Ramsey stoked in a second before his blistering strike, with the tempo dropping following the restart when the Welshman and Mathieu Flamini had made way for youngsters, both players rested as a precaution against injury.
Although Galatasaray scored a late consolation free-kick from Wesley Sneijder, Podolski grabbed a fourth on the break deep into stoppage time to give the English side a memorable victory.
Arsenal will, though, face one of the top seeds in Monday's draw for the last 16 of the Champions League, having finished as runners-up in Group D behind Borussia Dortmund.
Before February's European tie, by which time the likes of Mesut Ozil and Theo Walcott are expected back from injury, Ramsey accepts Arsenal must regain their Barclays Premier League form, with Wenger's men currently sixth following Saturday's 3-2 defeat at Stoke.
"I am getting sharper in every game, am feeling good and hopefully now I can play my part as they team go on a run," said Ramsey, who scored his first goal since the end of August at Stoke.
"That is the thing we need to do now.
"We have a busy couple of weeks coming up now and hopefully we can take full advantage of them, and hopefully take maximum points throughout December."
Wenger came in for some fierce personal criticism from the club's own supporters who waited for the team to board the train back to London on Saturday evening.
Ramsey felt the squad owed their under-fire manager a response out in Turkey.
"Every player here wants to work hard for him, we have proven that again here," the midfielder said.
"He has been under some unfair criticism, but we are all out there, are in it together
We wanted to get the result for us and for him.
"Whenever we go into a game, he knows our qualities, always believes in us and gives us a great feeling.
"Every time we go out there we are representing ourselves, our club and our manager."
Ramsey, who expects to shake off a tight hamstring for Saturday's visit of in-form Newcastle, had remained modest in his initial post-match reaction on Tuesday night.
But having seen the sublime finish replayed over and over again, the Wales midfielder hailed the goal as the best of his career so far.
"I have always got into goalscoring positions, but now I have found my composure more in front of goal," he said.
"As soon as I hit it, I thought it had a chance of going in and thankfully it went into the top corner.
"(Of my other goals before) I liked the volley at Norwich (in the final match of the last Premier League season), probably that one (was my favourite).
"But I have seen this goal back now, and it is definitely the best I have scored."
Ramsey, who also netted in Arsenal's 2013 Champions League play-off win at Fenerbahce, added: "I like playing in Istanbul - I have scored a few goals here now and I would like to play them every week if I could."
Source : PA