Borussia Dortmund can allow themselves to believe again after notching their first win in Group F, Kevin Grosskreutz making the difference for the faltering German giants against Olympiacos FC. Beaten in their two previous UEFA Champions League outings, the Bundesliga title holders desperately needed a victory to kick-start their campaign. The hunger told with just seven minutes gone as Grosskreutz found the net from distance. That early intensity soon faded, however, with Olympiacos providing intermittent danger of their own. The hosts greeted the final whistle, confirming their rise above their opponents into third spot, with relief. Jürgen Klopp encouraged Dortmund\'s fans to come in good voice for this crucial match and it soon became clear his message had got through. Colourful, committed and above all loud, the locals were repaid with a dynamic start from their side. Ivan Periši? scooped over an early chance before Grosskreutz collected Mario Götze\'s pass 20 metres out and drove thrillingly past surprise starter Balázs Megyeri in the Olympiacos goal. Grosskreutz himself was an unexpected, inspired, choice ahead of Shinji Kagawa, but Olympiacos threatened to cancel out his maiden European strike not long after, Kevin Mirallas forcing Roman Weidenfeller to save low to his right following a counterattack. François Modesto then volleyed over after Rafik Djebbour had headed a free-kick back across goal, and Olof Mellberg nodded a corner wide as the visitors ended the half on the front foot. Encouraged by their growing influence on the game, Olympiacos had the first look on goal after the break too. German midfielder José Holebas drew a diving save from Weidenfeller before 18-year-old Moritz Leitner, filling in for the injured Sven Bender in midfield, twice tried his luck from distance at the other end. Neither team seemed capable of locating the guile needed to get close to goal and, when Robert Lewandowski finally did for Dortmund, his chance sprang from an under-hit Holebas back pass rather than a moment of magic. Stealing in ahead of Megyeri, the industrious forward could only curl against the post from close to the byline. Eager to make up for his lapse, Holebas then headed narrowly off target from a corner. Desire and determination were gaining the upper hand on skill and creativity, but Dortmund demonstrated the tenacity required to protect their lead. Their next task will be to close on the top two at Arsenal FC on 23 November, when Olympiacos travel to Olympique de Marseille.