The result left the Germans second in the group on four points, behind Manchester United on nine following the English champions' 1-0 win over CSKA Moscow. Besiktas are bottom with just one point.
Wolfsburg dominated the game until striker Grafite was sent off for hitting an opponent late in the second half as the Turks settled back waiting for a chance to break.
"We did not score when we could have. I think we were unlucky as well," said Wolfsburg coach Armin Veh. "Our crosses were a bit too long. We seemed to play well up until the box. We wanted those three points."
The hosts came close after 10 minutes when striker Edin Dzeko, left completely unmarked in the box, connected with a deep Zvjezdan Misimovic cross but his header narrowly sailed over the bar.
Besiktas, who had lost all their previous matches against Bundesliga teams, quickly responded with a chance of their own but Ibrahim Kas's volley was blocked by keeper Diego Benaglio.
With the Turkish side built around a compact defence waiting to launch quick breaks mainly with Nihat Kahveci, Misimovic continued to feed fellow Bosnian Dzeko with crosses from out wide.
The German champions laid siege to the Turkish goal early in the second half, with Christian Gentner firing just over the bar five minutes after the restart. Dzeko hit the near post three minutes later with a low drive from the left.
The Germans were reduced to 10 men in the 74th minute when Brazilian forward Grafite, struggling for position in the box, struck Kas in the face with the back of his hand.
"We still have the keys for the next round in our hands. We are still in the running," said Wolfsburg defender Sascha Riether.
