Del Potro, seeded second, edged Michael Llodra 3-6, 7-6 (7-4), 7-5 in more than 2 1/2 hours. Del Potro had a handful of break opportunities but didn't finish one off until the 11th game of the third set.
Del Potro only lost his serve once, which allowed Llodra to take the first set. Del Potro pulled even by taking the second-set tiebreaker and advanced by holding serve after the late third-set break.
No. 6-seeded Gilles Simon, despite being good on just half of his first serves, beat Roberto Bautista-Agut 6-3, 6-1. Simon took 61 percent of the points both serving and receiving.
Jerzy Janowicz, the seventh seed, completed second-round play with a 7-6 (7-0), 6-3 win over Julien Benneteau. He broke the match open with the shutout in the tiebreaker and won eight of the first 10 points in the second set in taking a lead he wouldn't lose.
Janowicz takes on top-seeded Tomas Berdych and Tursunov meet Gilles Muller in the quarterfinals in the top half of the draw. Del Potro plays Simon and No. 3-seeded Jo-Wilfried Tsonga faces Bernard Tomic in the other quarterfinals.