Leipzig, winners in 2022 and 2023 as well as finalists in 2021, were reduced to 10 men early in the second half after Yussuf Poulsen was sent off following a second booking.
Cerny met almost no resistance when he sprinted into the box to latch onto a perfect Tiago Tomas through ball and rifle into the top corner in the 14th minute.
The Czech winger should have scored a second goal 10 minutes later when a misunderstanding in the Leipzig defence sent him clear on goal once more but he miskicked and fired wide.
Leipzig looked more aggressive after the break and hit the woodwork through David Raum.
But any hope of a comeback went out the window in the 56th when Poulsen got his marching orders following a clumsy foul on Aster Jan Vranckx who had snatched the ball away from the Dane.
In another battle of Bundesliga clubs VfB Stuttgart booked their third-round spot, with a 1-0 win over Champions League club Union Berlin, who have now lost their last 11 matches across all competitions.
Bayern Munich travel to Saarbruecken on Wednesday while Borussia Dortmund host Hoffenheim.
Check out the game summary from Wolfsburg's win with Flashscore.
