Demba Ba's hat-trick helped the Turkish side win 3-1 on the night and 5-2 on aggregate.
All three goals came in true poacher's fashion, with the Senegalese striker capitalising on errors and finishing from close range for two of them.
First, the Feyenoord defence gave the ball away in their own half and Ba's fumbled finished crept over the line to give his side the lead.
The Dutch hit back to make it 1-1 but the former Chelsea striker later put Besiktas back in the lead with a tap in after he got onto the end of a cross from the left.
And it was another defensive error that gifted Ba his third when a pass from a Feyenoord defender found its way perfectly into the 29-year-old's path.
Ba joined Besiktas last month for a £4.7 million fee, ending his one-and-a-half year stay at Stamford Bridge after moving to the Blues from Newcastle United.
Chelsea have also sold Romelu Lukaku for a fee believe to be around £28 million this summer, while they have brought in Diego Costa, as well as re-signing club legend Didier Drogba.
Besiktas are now safely into the Champions League play-offs, where success will see them into the competition's group stages.