The Brazilian full-back rounded off a solid away performance at the Veltins Arena with a powerful strike into the top corner, doubling the lead given to Real by Cristiano Ronaldo.
Ronaldo headed home Daniel Carvajal’s first-half cross for his sixth goal of the tournament, and 39th in all competitions this season.
However, the defending champions know they have another tough test at The Santiago Bernabeu before they can celebrate reaching the quarter-finals.
"In the Champions League anything can happen," Marcelo told AS after the game.
"We have humility and know we must work to win the tie. We fought hard and Schalke are a great team.
"We have a great advantage of two goals, but nothing is decided. Real Madrid must always go to the end [final] and we are on the way."
Meanwhile, Carlo Ancelotti was delighted to have secured a first-leg victory and praised his side’s performance against a resolute Schalke side.
"We started well and after the first goal we controlled the game well," he said. "In the end it was a good night for us."
Schalke’s unenviable task in the Spanish capital comes on March 1.
