Stoke manager Tony Pulis said his side were comfortable .
"It was a great performance," Pulis told BBC Radio Stoke. "I thought the lads were brilliant.
"There was a little bit of a lapse at the end but that's a little bit of tiredness. They huffed and puffed a little bit but we coped with it."
Second-half goals from Dean Whitehead and Peter Crouch maintained Stoke's four-point lead at the top of Group E.
Roberto Colautti's stoppage-time effort was not enough to stop the Potters from registering a third win in four group matches.
Besiktas jump into second place in the table after their 1-0 home win against Dynamo Kiev.
Stoke require a point from their final two matches to secure their place in the last 32, while a win in either of their remaining two games will see them confirmed as group winners.
Pulis's side face Dynamo Kiev at the Britannia Stadium on 1 December, before ending the group in Turkey against Besiktas 13 days later.
"Kiev at the Britannia now is a cup final," added the Stoke boss.
"If we don't get beat, we'll go through. It's as simple as that, so it's a massive game for us. They are a good side."
Defender Danny Higginbotham played the full 90 minutes on his first appearance since April after recovering from a cruciate ligament injury.
"I told him about two weeks ago that this was the game I was looking at [to bring him back] so I told him to get himself ready for it," said Pulis.
"He tired in the last 20 minutes, along with one or two others.
"Wilson Palacios got 65 minutes, he isn't as sharp as we want him to be but he needs to play games to do that."
Stoke return to Premier League action on Sunday when they visit struggling Bolton.