Wolfsburg and Leipzig both qualified for the quarter-finals of the German Cup on Wednesday night.
The in-form Wolves, in third place in the Bundesliga, have won their last four games in all competitions without conceding a goal.
Schalke keeper Ralf Faehrmann did well to save Wout Weghorst's 40th-minute penalty but the Dutchman stabbed in on the rebound for the winner.
Nagelsmann hails Bayern commitment after win over Leverkusen: 'They were fully into it'
The Royal Blues, in last place in the league, should have equalised on the stroke of halftime but American teenager Matthew Hoppe was denied from close range by keeper Koen Casteels with a sensational reflex save.
Schalke battled hard and had their share of chances after the break, going close again through Mark Uth midway through the second half, but the striker failed to connect with a cutback in front of goal.
Despite a frantic finale and pressure from Schalke, Wolfsburg managed to hold on for the win.
Leipzig had a far easier evening against Bochum, with Denmark striker Poulsen scoring twice after Amadou Haidara and Marcel Sabitzer had given the hosts a two-goal cushion in the first half.
Borussia Moenchengladbach joined them in the last eight after coming from a goal down to beat VfB Stuttgart 2-1.
Stuttgart's Silas Wamangituka put the hosts ahead with a sensational 70-metre solo effort after two minutes, almost identical to a goal he scored in the Bundesliga last week.
But Marcus Thuram levelled on the stroke of halftime with a curled shot and Alassane Plea completed Gladbach's comeback five minutes after the restart.

Juventus still chase Pogba but have 'luxury' Plan B – Euro Papers

Xavi frustrated at Barca injury list as club tries to go top of La Liga
Premier League
Arteta ready for 'very special' North London Derby