The Pole was making his Bayern bow following his Bosman transfer from bitter rivals Borussia Dortmund, and looked sharp in attack, keeping home goalkeeper Michael Ratajczak busy in a goalless first half.
However, substitute shot-stopper Marcel Lenz was powerless to prevent Lewandowski opening his account just after the hour mark, following good work from Rafinha.
A frustrating outing saw Bayern, still without their World Cup contingent, struggle to create opportunities playing a 3-5-2 system with just one recognised centre-half on the pitch in the shape of Holger Badstuber, whose comeback from injury was boosted by an 85-minute run-out.
And 20-year-old winger Fabian Schnellhardt grabbed a deserved draw for Duisburg, curling home a fine strike.
Bayern made a good start with regular left-back David Alaba probing from a central midfield role that he often operates in for Austria at international level.
Lewnadowski went close eight minutes in, latching onto Lucas Scholl's downward volley, but Ratajczak was alert to flick away the striker's flicked header.
Alexander Sieghart saw a good effort saved for Bayern before Duisburg raced up the other end and should have taken the lead, only for Zlatko Janjic to inexplicably miss from six yards.
A quick start at both ends belied the rest of the half as Bayern set up camp in Duisburg's half but found centre-backs Christopher Schorch and Thomas Meissner in stubborn mood.
The first period ended goalless and Bayern's struggles continued immediately after the break, Duisburg calling Tom Starke into action through Scorch and Janjic.
But Bayern's class finally told as Rafinha clipped a neat delivery in from the right flank and Lewnadowski touched the ball away from Lenz before providing a low finish.
The hosts were determined to give a good account of themselves, though, and produced the game's outstanding moment through Schnellhardt.
Drifting in from the right channel, the Germany Under-20 international touched the ball onto his left foot before curling a superb 25-yard effort out of Starke's reach.
Michael Eberlein wasted a good opening soon after when racing through on goal, with the winger's touch letting him down.
Lenz denied Lewandowski in the closing stages, diving at the Poland striker's feet to preserve a creditable result for the 3. Liga side.
