The Spanish outfit will travel to Turkey in a dominant position but will be left ruing Simao's strike moments after the break that keeps the Black Eagles' slim hopes alive
The Turks were looking to win for the first time in Spain, and despite a goal from the winger against his former club, they left Spain knowing that their involvement in the competition is hanging by a thread.
Atleti opened a seemingly unassailable three-goal lead by half-time thanks to a brace from Toto Salvio before Adrian's remarkable solo effort. Diego Simeone's men were in full control of the tie but Simao's wondrous volley at the start of the second period keeps Besiktas within touching distance of their Spanish opponents.
Both sides showed attacking intent early on as Falcao narrowly poked wide of the target after lovely work from Salvio on the right. Manuel Fernandes then stung the palms of Thibaut Courtois with a rasping drive from distance, an effort that proved to be all the visitors could muster in the opening 45 minutes.
Following a remarkable miss moments before it wasn't a long wait for Salvio to make amends. The Argentine latched onto a perfectly lifted pass before controlling instantaneously allowing him to take the ball towards goal. He then managed to evade the full-back before slipping his shot underneath a hapless Cenk Goren.
Salvio bagged a second goal within three minutes of his first with a truly exquisite strike. Following Gabi's gorgeous through ball, the winger stood up to Goren before floating a superb chip beyond his grasp.
Los Colchoneros, though, were not finished and when Adrian capitalised on a sloppy pass in the centre circle, what came next was inevitable.
The Besiktas defence stood off the marauding Spaniard, before he bamboozled Egeman Korkmaz with his slick footwork. He then unleashed a venomous strike that smashed the underside of the bar before nestling in the back of the net.
Returning for the second half, Besiktas needed to find an early strike, and it came from Simao. The Portuguese capitalised on Atleti's failure to clear a corner by rocketing a perfectly-timed volley to net an invaluable away goal.
Carlos Carvalhal's side showed a continued improvement after the break and Simao's low cross nearly brought Besiktas to within a single goal, only for Mustafa Pektemek to put his effort wide.
Atleti rediscovered their form as the half continued and had several opportunities to extend their lead further but Falcao, Koke and Salvio all wasted openings to re-establish their three goal lead, whilst Goren was lucky not to see his clearance ricochet back off Falcao into an empty net.
The Spanish side were left thanking their keeper for a two goal advantage to take to Turkey in a weeks time for the return leg, with Courtois called upon to make a vital save denying Filip Holosko.