The Gunners were stretched by Slaven Bilic’s well-drilled outfit, who almost took the lead right from kick-off at the Ataturk Olympic Stadium through a long-range effort by former Chelsea striker Demba Ba.
However, the visitors held out and – but for some poor finishing by Olivier Giroud – could came netted an away goal, with substitute Alex Oxlade-Chamberlain seeing his shot touched onto the post late on
Ramsey, who scored a stoppage-time winner against Crystal Palace on the opening day of the Barclays Premier League season, was dismissed for a second yellow card with ten minutes left.
Arsenal, though, will welcome back Germany World Cup-winning trio Mesut Ozil, Per Mertesacker and Lukas Podolski ahead of next week’s second leg at the Emirates Stadium, when they will be out to secure a remarkable 17th successive campaign in the lucrative group stages of Europe’s elite club competition.
It had, however, almost been a nightmare start for the English side.
After the ball was rolled from kick-off, Ba sent an audacious effort looping towards the top corner, which Wojciech Szczesny clawed up onto the crossbar.
Besiktas may technically have been playing away, with their Vodafone Arena home being redeveloped, but you would not have known it given the ferocity of the Turkish fans.
Arsenal were reduced to ten men on 80 minutes after Ramsey collected a second yellow card for pulling back Oguzhan Ozyakup, the former Gunners midfielder, and will now miss the return leg.
The visitors almost won it when Oxlade-Chamberlain, on for Alexis Sanchez, cut in from the right and drilled the ball goalwards, but Zengin touched it onto the post at full stretch.
Bilic was sent to the stands just before the final whistle, knowing there will be all to play for in north London next week.