Arsenal scraped into the group stage of the Champions League on a night of high anxiety at the Emirates Stadium that saw Alexis Sanchez open his Gunners account.
Arsene Wenger's team missed a succession of chances to put the qualifier beyond the reach of Besiktas following a goalless draw in the first leg in Istanbul, with a 1-0 win putting Arsenal through.
Sanchez, Santi Cazorla and Alex Oxlade-Chamberlain failed to score when it was harder to miss amid the mayhem of a roller-coaster second half in which Mathieu Debuchy was sent off for collecting a second yellow card.
Frantic Arsenal almost paid the ultimate price as they were over-run time and again by Besiktas who sought the away goal that would secure a prized European scalp.
The Turks' coach Slaven Bilic, sat in the stands due to his touchline ban for arguing with referee Milorad Mazic in the first leg, watched as Demba Ba crashed a great chance into the side netting.
It was the best of Besiktas' opportunities, although Bilic was furious that a penalty was not awarded when Ramon Motta appeared to be clipped from behind by Jack Wilshere.
Sanchez's goal on the stroke off half time enabled Arsenal to progress into the Champions League proper for a 17th successive season, but they rode their luck against spirited opposition to subject their fans to a nail-biting night.