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."
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.
"We still have the keys for the next round in our hands. We are still in the running," said Wolfsburg defender Sascha Riether.
