Saint Petersburg, Russia (SportsNetwork.com) - Borussia Dortmund took a big step toward reaching the Champions League quarterfinal by running out to a 4-2 victory at Zenit St. Petersburg on Tuesday.

The German side made a bright start to the match, capitalizing on a couple of defensive miscues early on to grab a two-goal lead inside the opening six minutes.

Henrik Mkhitaryan opened the scoring in the fourth minute, and Marco Reus doubled Dortmund's advantage just one minutes later by firing home a lay-off from Kevin Grosskreutz.

The visitors appeared to be in cruise control until Zenit pulled one back in the 57th minute as Oleg Shatov collected a rebound off the post and slammed home a left-footed shot into the bottom corner, but Dortmund restored its two- goal lead four minutes later when Robert Lewandowski turned in a square pass from Lukasz Piszczek.

Zenit clawed back to within one after Piszczek was whistled for a dubious foul in the box, an infraction that allowed Hulk to hammer home from the spot in the 69th minute.

But the Russian side was left to rue some more poor defending just two minutes later as Reus released Lewandowski on the right side of the box before the Poland international slotted a shot past Juri Lodigin.

Dortmund's emphatic victory leaves Zenit with a mountain to climb for the return match at Signal Iduna Park on March 19 as the Russian club must overturn the two-goal aggregate deficit.

In Tuesday's other Champions League contest, Manchester United turned out a dreadful display in a 2-0 loss at Olympiakos.

The home side took the lead in the 38th minute when Alejandro Dominguez unleashed a shot that took a deflection on its way past David De Gea.

The margin was doubled nine minutes into the second half when some poor defending from United afforded Joel Campbell the time and space to curl home a superb finish from distance.

Manchester United struggled to create much going forward and ultimately paid the price as the Red Devils return home for the second leg on March 19 with a two-goal deficit and no away goals.