Third seed Wawrinka, winner of the 2014 Australian Open and 2015 French Open, overpowered the 63rd-ranked Marchenko, who reached the fourth round when 14th-seeded Nick Kyrgios retired with a hip injury while trailing two sets to one.
Marchenko was treated twice during Monday's match for his right knee, which was taped between the second and third sets and massaged during the third-set changeover at 2-1, but he battled on to force a fourth set.
The victory by the hard-hitting Swiss set up a clash with big-serving del Potro, who won 6-3 3-2 when eighth seed Dominic Thiem of Austria retired with a knee injury.
"It's going to be great to play (del Potro)," Wawrinka said in an on-court interview. "He beat me this year at Wimbledon. He's back after so many injuries, so it's good to see him playing so well again.
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It will be their first meeting on a hard court, and the Swiss will be looking to avenge his second-round loss at the All England Club to the Argentine, who has regained his form after a long struggle with an injured left wrist.
"It's going to be a great challenge for me to play him here on the hard court for the first time," said Warwinka. "Excited to play against him and hopefully I can keep going here."
(Editing by Frank Pingue)
