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Second seed Djokovic, who is tipped to relieve five-time champion Rafael Nadal of his Roland Garros title and top ranking, was leading Victor Hanescu 6-4, 6-1, 2-3 when the Romanian quit their second-round tie with a leg injury.
"It's never easy to see an opponent giving up. It's bad luck for him. I played well and it's good to spend as little time on court as possible," said Djokovic.
The Australian Open champion, who has also won all four Masters titles in 2011, now stands five wins away from equalling Guillermo Vilas's record for a winning streak.
He is also only three away from John McEnroe's 1984 record for an undefeated start to a season.
Argentine 25th seed Del Potro, the former US Open champion and a 2009 semi-finalist in Paris, made the last 32 with a 6-3, 6-2, 6-4 win over Slovenia's Blaz Kavcic.
Del Potro missed last year's Roland Garros to recover from wrist surgery and was almost forced out of this edition because of a hip injury.
The former world No 4's ranking slipped to 485 during his time off tour, but he has been in fine form in 2011, winning tournaments at Delray Beach and Estoril.
"It should be a beautiful match with Novak. It'll be a special occasion against a great player. He's the favourite, but I will try and fight for the victory," said the Argentine.
Roger Federer, for one, was looking forward to the Djokovic-Del Potro clash, even if the Serb has won all of their three previous meetings without dropping a set.
"If Juan Martin hadn't been injured with his wrist, maybe he would have won the French Open last year," said Federer.
Third-seeded Federer won 13 games in succession as the 16-time Grand Slam title-winner easily disposed of French wild card Maxime Teixeira 6-3, 6-0, 6-2 in his second-round tie.
The 2009 champion will next face Serbian 29th seed Janko Tipsarevic, who beat Spain's Pere Riba.
The Swiss great overcame an early break before breezing through in just 84 minutes, leaving Teixeira, playing in his first Grand Slam event, looking every inch the world 181.
"He fought really hard and was trying his best," said Federer.
"It was a good match. I'm happy with the way I played. I feel like I am in the tournament now."
Next up is Tipsarevic, the colourful Serb who stretched Federer to five sets in the 2008 Australian Open third round.
"He's a dangerous player, especially on the big courts against the big players," said Federer.
Also going through to the last 32 on Wednesday were Spanish seventh seed David Ferrer, French ninth seed Gael Monfils, Mikhail Youzhny, the Russian number 12 seed and French 13th seed Richard Gasquet.
Results on Wednesday from Roland Garros:
Mens Singles
Second Round
Roger Federer (3), Switzerland, def. Maxime Teixeira, France, 6-3, 6-0, 6-2.
Janko Tipsarevic (29), Serbia, def. Pere Riba, Spain, 6-1, 6-3, 6-0.
Sergiy Stakhovsky (31), Ukraine, def. Kei Nishikori, Japan, 6-1, 3-6, 6-3, 7-6 (3).
David Ferrer (7), Spain, def. Julien Benneteau, France, 6-3, 6-4, 6-2.
Gael Monfils (9), France, def. Guillaume Rufin, France, 6-3, 1-6, 6-1, 6-3.
Steve Darcis, Belgium, def. Philipp Petzschner, Germany, 7-5, 6-4, 6-4.
Juan Martin del Potro (25), Argentina, def. Blaz Kavcic, Slovenia, 6-3, 6-2, 6-4.
Thomaz Bellucci (23), Brazil, def. Andreas Seppi, Italy, 6-1, 6-2, 6-4.
Richard Gasquet (13), France, def. Marcel Granollers, Spain, 4-6, 6-3, 6-2, 6-4.
Mikhail Youzhny (12), Russia, def. Mikhail Kukushkin, Kazakhstan, 6-3, 7-5, 6-4.
Albert Montanes, Spain, def. Ruben Ramirez Hidalgo, Spain, 6-7 (5), 6-4, 6-1, 6-2.
Novak Djokovic (2), Serbia, def. Victor Hanescu, Romania, 6-4, 6-1, 2-3, retired.
Womens Singles
Second Round
Anastasia Rodionova, Australia, def. Edina Gallovits-Hall, Romania, 6-1, 6-4.
Sam Stosur (8), Australia, def. Simona Halep, Romania, 6-0, 6-2.
Gisela Dulko, Argentina, def. Tsvetana Pironkova (32), Bulgaria, 6-4, 6-2.
Caroline Wozniacki (1), Denmark, def. Aleksandra Wozniak, Canada, 6-3, 7-6 (6).
Julia Goerges (17), Germany, def. Lucie Safarova, Czech Republic, 2-6, 7-5, 6-2.
Bethanie Mattek-Sands, United States, def. Varvara Lepchenko, United States, 6-3, 2-6, 6-3.
Anastasia Pavlyuchenkova (14), Russia, def. Mona Barthel, Germany, 6-0, 7-6 (5).
Nuria Llagostera Vives, Spain, def. Alize Cornet, France, 6-0, 6-2.
Svetlana Kuznetsova (13), Russia, def. Irina-Camelia Begu, Romania, 6-1, 6-1.
Jelena Jankovic (10), Serbia, def. Vera Dushevina, Russia, 6-3, 6-2.
Rebecca Marino, Canada, def. Maria Jose Martinez Sanchez, Spain, 2-6, 6-3, 6-3.
Peng Shuai (29), China, def. Polona Hercog, Slovenia, 7-5, 6-1.
Daniela Hantuchova (28), Slovakia, def. Sara Errani, Italy, 6-1, 6-2.
Marion Bartoli (11), France, def. Olga Govortsova, Belarus, 6-4, 6-7 (1), 6-2.
