Tottenham started the game fairly composed and were happy to contain Besiktas.
Robbie Keane was dropping deep to form a five-man midfield on lots of occasions.
The visitors were in firm control of proceedings for the remainder of the first half, and deserved the game's opening goal.
Hossam Ghaly needed to rely on a touch of luck in converting Dimitar Berbatov's assist at the second time of asking, as his first effort bounced back off the goalkeeper.
Paul Robinson was then called into action as first he denied a fierce free kick, then somehow chased and punched the ball clear as it dropped dangerously above his goal line.
Besiktas came out with intent in the second half, but it was relatively shortlived.
Keane found Berbatov and the Bulgarian showed his class to twist and turn his way past the right back, then the goalkeeper, before slotting the ball home for Tottenham's second of the night.
The front pairing linked again soon after, this time Keane's volley struck into the ground, deflected back off the upright, but by then three points had already been secured.
Martin Jol: "We were very satisfied with the three points. It was a great experience for us with such a fanatical crowd. We said beforehand that we had to enjoy it, that was the main thing, to get a result and fight for every yard.
"We started off well, controlled the first half but we couldn't score more than one goal and that made it difficult against someone like Besiktas.
"Dimitar Berbatov then showed his extra quality, we scored the second goal at the right moment and then had three or four chances after that.
"We had to re-organise in midfield because we lost Didier Zokora late with a fever, but Tom Huddlestone came in and had a very good game together with Jermaine Jenas.
"Last season we scored goals at crucial moments and we hadn't done that so far this season, that's why it was important Hossam Ghaly scored the first goal and then Berbatov the second."
"I thought Hossam was excellent in the first half, the defence was excellent and we were too strong to concede goals. I was happy with the team performance.
"The crowd was second to none but we kept our heads cool and motivated to have a very good result."
"To be applauded off the pitch in Turkey was probably evidence that they rated us."
"We wanted to silence the crowd but after a couple of minutes we thought it would be impossible to silence a crowd like that."
Robbie Keane: "I was very proud because we knew before the game that it would be difficult. They were a good side and the crowd, I have to say, were something else - even when they were getting beat. Clapping us off after the game was really good of them."
"The lads were brilliant and I think we dominated the game. I was happy for Hossam, he showed tonight he is a good footballer. He's been playing well and deserved that goal for his work ethic. It came at a good time and in the second half we could have had a few more, but we've got the three points and that was the most important thing."
Hossam Ghaly: "It was my first goal for Spurs and for it to come in a big UEFA Cup game made it even more special. It was our first game in the group and it was good for me to score the goal that got us on our way to a win."
"We played a good game, we were organised and played with discipline. We kept our shape, Besiktas didn't have many chances to score, while we created openings for ourselves. We missed a couple and scored two so it was a good result for us."
"I didn't expect the home fans to applaud us off the pitch at the end after having won the game. We played in a fair way, played well and they respected us for it."
Danny Murphy: "It was a top performance against a good side, certainly one to remember. We'd watched them quite a lot beforehand on video and realised they have some quality players.
"Having played over here before I knew how difficult it is but the quality of our performance showed."
"Everyone to a man played well, everyone played near enough to their capabilities and we could have won by more."
"Their supporters kept going throughout and then still had the humility to clap us off at the end, which said a lot for them and a lot for our performance."
"We haven't been beaten now since the Liverpool game, we've played some good football in the last couple of games and here was probably the best 90 minutes we've played in a while."
Source: TottenhamHotspur.com