VfL Wolfsburg's out-of-form striker Grafite, the top scorer in the Bundesliga last season who is struggling this term, was shown a straight red card midway through the second-half for violent conduct and will be banned for at least the next game.
"We are a better team than that and we are bitterly disappointed not to win," said Wolfsburg's striker Edin Dzeko. "We should have scored, I think we were better than the 0-0 draw, but that is football."
With Manchester United winning 1-0 in Moscow to dominate the group and keep
their 100 percent record, the battle is now on for second place.
Moscow are third in the table on three points, while Wolfsburg are second on four points after three games as Besiktas picked up their first point of the competition and leaders Manchester United have a maximum nine points.
"The key to the next round is still in our hands and we need to make sure we don't hide in the next two games," said Wolfsburg defender Sascha Riether with the Wolves travelling to Istanbul on November 3 and then Moscow on November 25. "We are still in the fight and must make sure we stay in with a shout."
It was honours even at the end of the first-half as Wolfsburg threatened on several occasions with the aerial prowess of Dzeko a constant worry for the Besiktas back four, but his strike partner Grafite looked rusty.
The visitors produced little in the way of attacking football, but the Turks looked capable of scoring with Nihat Kahveci and Bobo both creating individual chances.
The Wolves squandered a gold-plated opportunity to take the lead on 53 minutes, when the home side poured forward in numbers and drew Besiktas veteran goalkeeper Rustu Recber, but somehow Christian Gentner managed to fire over the bar.
With the football turning into a lacklustre affair, the Turkish fans at least lit up a gloomy night at the Volkswagen Arena by setting off several flares which sent smoke billowing across the pitch.
Grafite was sent for an early shower on 73 minutes when he struck Besiktas defender Ibrahim Kas on the side of the face leaving Italian referee Roberto Rosetti with no choice but to send him off.
Despite the numerical advantage, Besiktas could not get a valuable away goal and there is still everything to play for on November 3 back in Istanbul.