Assuming he is close to fully fit, Del Potro, who is still working his way back up the rankings after wrist problems that nearly ended his career, will present a serious test of Murray's Roland Garros ambitions.
Juan Martin Del Potro again showed himself to be one of tennis' great sportsmen when he comforted distraught second-round opponent Nicolas Almagro at the French Open. After slamming his water bottle to the clay in frustration, Almagro returned to his chair - and was joined by del Potro, who hung around and offered words of encouragement to the new dad, whose son was born earlier this year.
Del Potro, who went on to guide Argentina to their first Davis Cup title, was always going to be a danger lurking for one of the top seeds as he continues to work his way back up the rankings after wrist problems nearly ended his career.
Del Potro had taken the first set of the second round clash 6-3 before Almagro claimed the next by the same score.
The Argentine helped a sobbing Almagro from the court and will now face Andy Murray in the third round.
Argentina's Del Potro is playing in his first French Open since 2012 having suffered a series of injuries.
"The second and third set was not easy, but I was ready with my game at the important moments when I needed, and it worked really good".
"Getting frustrated on the court is something that I have always battled with and always fought ever since - it was probably since I was 20, 21 years old - and it's more venting", Murray said. Try to think about your family, your baby. And I also hit a lot of balls out there, more than the first-round match.More news: Theresa May approval rating sinks as United Kingdom election race tightens
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"Today I think I got lucky, because I don't feel good enough with my body", he added. I know his game a lot, but I need to be in good shape and physically be stronger to hold a long match if we play a long match, long rallies.
World number 50 Klizan has already hit the headlines in Paris by being accused of faking an injury in his opener against French wildcard Laurent Lokoli.
British number two Kyle Edmund also progressed after beating Renzo Olivo 7-5 6-3 6-1.
Things weren't quite so straightforward for ninth seed Agnieszka Radwanska, who needed almost two and a half hours to beat Belgian qualifier Alison Van Uytvanck 6-7 (3) 6-2 6-3. Apparently close to retirement one minute, Klizan recovered from dropping the fourth set to love to win in five.
Pliskova would do well to get there since clay isn't her preferred surface.
In the women's draw, Ukrainian fifth seed Elina Svitolina dropped the opening set before she ousted Bulgaria's Tsvetana Pironkova 3-6, 6-3, 6-2.
Third seed Simona Halep eased through with a routine win against Germany's Tatjana Maria.