Tottenham started stronger and had a goal disallowed in the 12th minute when Bulgarian striker Berbatov was ruled offside after knocking in a rebound from the Turkish team's Croatian keeper Vedran Runje.
Twenty minutes later the London side took the lead when a shot from Egyptian midfielder Ghaly again rebounded off Runje and then took a fortunate bounce back off Ghaly into the net.
Besiktas went close in the 37th minute when a powerful free kick from defender Gokhan Zan tested Tottenham keeper Paul Robinson.
The visitors doubled their lead in the 63rd minute when Berbatov made up for his earlier disallowed goal.
The Bulgarian international was released on the right and skilfully rounded a defender and the goalkeeper before slotting the ball into an empty net.