Hossam Ghaly and Dimitar Berbatov were on the mark for Tottenham as they won their opening Uefa Cup Group B game.
Ghaly scored his first goal for Spurs
Ghaly's first goal for Spurs involved some luck as goalkeeper Vedran Runje saved his initial shot, only for the ball to hit the Egyptian and loop in.
It was a Berbatov pass that released Ghaly and the Bulgarian capped a fine display with a solo second-half goal.
Sent clear by Robbie Keane, who later hit the bar, Berbatov first beat Baki Mercimek and then Runje before netting.
If there was an element of fortune in Spurs' opening goal, there was nothing lucky about this victory.
From the start Spurs dominated proceedings, with Ghaly, Danny Murphy, Tom Huddlestone and Jermaine Jenas controlling midfield.
Spurs' defence was equally dominant and Besiktas were reduced to trying their luck with long-range efforts, only twice drawing saves from Spurs goalkeeper Paul Robinson.
Berbatov had the ball in the net as early in the 12th minute, but he was offside when Runje pushed a Murphy shot into the Irish Republic striker's path.
Berbatov's link-up play ensured Spurs were always able to find plenty of space behind the Besiktas defence.
The Bulgarian played a key role in Ghaly's goal, taking out three Besiktas players with a clever turn and pass to release the Egyptian.
Runje was out quickly to block Ghaly's shot, but the Besiktas keeper could not do nothing to stop the rebound going in.
Just before the break another clever Berbatov pass released Murphy, whose angled shot was pushed past the post by Runje.
Berbatov scored his first goal in Europe for Spurs
Besiktas rarely threatened before the break, though Burak Yilmaz tested Paul Robinson with a fierce free-kick.
The Spurs keeper was unable to hold Yilmaz's shot, but he was up quickly to punch the ball clear.
After the break Besiktas looked more coherent going forward and Serdar Kurtulus flashed a shot narrowly wide.
Just as the Turkish side suggested they might have a chance of getting back into the game, Berbatov ran free to collect Keane's volleyed pass.
The Bulgarian turned inside Mercimek leaving the Besiktas player on the floor and then danced round Runje before sidefooting home.
Soon after Berbatov's goal, Keane rattled the crossbar after some sloppy Besiktas defending as Spurs threatened to run riot.
Keane might have added to Spurs' goal tally, but the Irishman's finishing was less assured than his striking partner Berbatov.
With four minutes left Robinson was called into action for a second time, saving another Yilmaz effort.
Spurs manager Martin Jol:
"We couldn't score the second and then we had a flash of quality from Berbatov and that was what we needed.
"We started off well and we got that first goal through Ghaly, but we knew that wasn't going to be enough.
"The crowd were very noisy - it was impossible to keep them quiet, but in the end we were applauded off. We achieved what we wanted."
Besiktas: Runje, Kurtulus, Sedef (Bobo 46), Zan, Yilmaz,
Mercimek, Marcio Nobre, Ricardinho, Uzulmez, Tatan (Akin 66),
Subs Not Used: Sahin, Dogan, Gulec, Tandogan, Gunes.
Booked: Tatan, Toraman.
Tottenham: Robinson, Chimbonda, Dawson, King, Assou-Ekotto,
Ghaly (Lennon 83), Huddlestone, Jenas, Murphy (Ziegler 80),
Berbatov (Defoe 90), Keane.
Subs Not Used: Cerny, Davids, Stalteri, Gardner.
Booked: Chimbonda, Ghaly.
Goals: Ghaly 32, Berbatov 63.
Ref: Nicolai Vollquartz (Denmark).