The home side's cause was not helped by a red card to Helder Barbosa during the first half. The 24-year-old was handed his marching orders in the 29th minute for a second bookable offence.
Turkish side Besiktas made their numerical advantage count in the 37th minute when centre-back Tomas Sivok guided the ball into the net from close range.
Former Atletico Madrid winger Simao scored his side's second in the 58th minute following a passing move.
The two teams will meet next week for the return leg in Turkey.