The Polish striker put Dortmund 3-1 ahead on the hour-mark before netting with just under 20 minutes remaining to give the German side a handy two-goal advantage going into the return leg.
As the Champions League away days continued, Dortmund skipped away to an early two-goal lead at the Petrovsky Stadium, in Zenit's first fixture in a month, when Henrikh Mkhitaryan and Marco Reus had the visitors fully in the ascendency by the fifth minute.
Mkhitaryan was the recipient of some brilliant play from Reus with the German making a persistent run before laying off for the Armenian to fire home.
Just over a minute later, Reus got on the scoresheet when he slotted Kevin Grosskreutz's nice lay-off beyond Zenit gloveman Yuri Lodygin's reach.
Luciano Spalletti's Zenit were able to hit back just prior to the hour-mark when Oleg Shatov rifled home from close range after a goalmouth scramble fell to him following Salomon Rondon's effort which deflected off the upright.
Lewandowksi then got in on the act to restore Dortmund's two-goal lead when he stroked home after playing a neat one-two with fellow Pole Lukasz Piszczek in the 61st minute before the latter was penalised for fouling Viktor Fayzulin in the area.
That allowed Hulk to step up to the spot and smash his penalty into the corner off the crossbar for a 3-2 scoreline in the 69th minute but Lewandowski had the final say by finishing clinically from an angle after being found by Reus.
The four away goals for BVB will be of great assistance when they return to Dortmund for the second bout at Signal Iduna Park on March 19.
The win on the road for Dortmund had made it five from five away wins in the first knockout phase of this season's Champions League prior to Olympiakos scoring a home victory over Manchester United.
2013/14 UEFA Champions League - Round of 16 first leg
Zenit St Petersburg (RUS): 2 (Oleg Shatov 57', Hulk (p) 69') Borussia Dortmund (GER): 4 (Henrikh Mkhitaryan 4', Marco Reus 5', Robert Lewandowski 61'/71') Petrovsky Stadium, St Petersburg, Russia - 15,099
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