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The Serbian was dragged into a first-set tiebreak, which he won 7-3, before he gradually outpaced the world No 97 with a string of thundering winners.
Instead of trying to deflect all the pressure and attention that has been building up towards his title bid, Djokovic chose to embrace a sentiment voiced by tennis great Billie Jean King.
"Pressure is always present, and the way I look at it, it is a privilege and it's a challenge," Djokovic told a news conference.
"So you need to try to understand and learn how to deal with it, and if you feel pressure, that means that you're doing something that is right.
"So I'm happy - I'm happy to be where I am at this moment."
Djokovic, who could meet third seed Roger Federer in the semi-final in a rematch of last year's epic last-four tie, is taking a down-to-earth approach to his quest.
"It doesn't give me an extra negative pressure. I really think it's a challenge and something to embrace and to enjoy," he said.
"I'll try to go step by step."
Starace put up a decent fight in the opening set and was only broken in the fifth game of the second before Djokovic, who did not face a single break point throughout, found his stride on a sundrenched Court Philippe Chatrier and raced home in just over two hours.
Results from the second day of the 2012 French Open at Roland Garros on Monday (x denotes seeded player):
Men
First Round
Florent Serra, France, def. Feliciano Lopez (15), Spain, 5-0, retired.
Martin Klizan, Slovakia, def. Frank Dancevic, Canada, 4-0, retired.
Marcel Granollers (20), Spain, def. Joao Sousa, Portugal, 6-2, 3-6, 6-3, 6-4.
Blaz Kavcic, Slovenia, def. Lleyton Hewitt, Australia, 7-6 (7/2), 6-3, 6-7 (4/7), 6-3.
Malek Jaziri, Tunisia, def. Philipp Petzschner, Germany, 6-3, 7-5, 7-6 (9/7).
Mikhail Kukushkin, Kazakhstan, def. Ernests Gulbis, Latvia, 6-4, 7-6 (7/4), 5-7, 2-6, 6-4.
Andreas Seppi (22), Italy, def. Nikolay Davydenko, Russia, 6-3, 7-6 (7/5), 7-5.
Roger Federer (3), Switzerland, def. Tobias Kamke, Germany, 6-2, 7-5, 6-3.
Lukasz Kubot, Poland, def. Karol Beck, Slovakia, 7-5, 6-2, 7-5.
Adrian Ungur, Romania, def. David Nalbandian, Argentina, 6-3, 5-7, 6-4, 7-5.
Horacio Zeballos, Argentina, def. Eric Prodon, France, 6-7 (8/10), 6-3, 6-3, 6-2.
Kevin Anderson (31), South Africa, def. Rui Machado, Portugal, 7-6 (7/2), 6-7 (6/8), 4-6, 6-1, 11-9.
John Isner (10), United States, def. Rogerio Dutra Silva, Brazil, 6-3, 6-4, 6-4.
Jesse Levine, United States, def. Benjamin Becker, Germany, 7-5, 6-2, 6-4.
Novak Djokovic (1), Serbia, def. Potito Starace, Italy, 7-6 (7/3), 6-3, 6-1.
Michael Llodra, France, def. Guillermo Garcia-Lopez, Spain, 7-6 (7/5), 6-2, 3-6, 6-3.
Bernard Tomic (25), Australia, def. Andreas Haider-Maurer, Austria, 7-6 (7/5), 6-3, 6-3.
Santiago Giraldo, Colombia, def. Alejandro Falla, Colombia, 5-7, 6-2, 6-4, 7-6 (7/4).
Arnaud Clement, France, def. Alex Bogomolov Jr., Russia, 6-2, 3-6, 4-6, 7-6 (7/2), 5-4, retired.
Viktor Troicki (28), Serbia, def. Thomaz Bellucci, Brazil, 4-6, 6-3, 5-7, 6-3, 6-2.
Tomas Berdych (7), Czech Republic, def. Dudi Sela, Israel, 6-3, 6-4, 6-1.
Milos Raonic (19), Canada, def. Ruben Ramirez Hidalgo, Spain, 6-4, 6-2, 6-2.
Gilles Simon (11), France, def. Ryan Harrison, United States, 3-6, 7-5, 6-4, 6-1.
Paul-Henri Mathieu, France, def. Bjorn Phau, Germany, 2-6, 4-6, 6-4, 6-3, 6-0.
Philipp Kohlschreiber (24), Germany, def. Matthew Ebden, Australia, 6-4, 6-4, 7-6 (7/4).
Leonardo Mayer, Argentina, def. Olivier Rochus, Belgium, 6-3, 6-4, 2-6, 6-4.
Brian Baker, United States, def. Xavier Malisse, Belgium, 6-3, 7-6 (1), 7-6 (5).
David Goffin, Belgium, def. Radek Stepanek (23), Czech Republic, 6-2, 4-6, 2-6, 6-4, 6-2.
Tommy Haas, Germany, leads Filippo Volandri, Italy, 6-3, 0-6, 6-4, 4-2, susp., darkness.
Alexandr Dolgopolov (16), Ukraine, vs. Sergiy Stakhovsky, Ukraine, 7-6 (7/4), 4-6, 6-7 (4/7), 6-3, susp., darkness.
Women
First Round
Dominika Cibulkova (15), Slovakia, def. Kristina Mladenovic, France, 6-2, 6-1.
Lauren Davis, United States, def. Mona Barthel (30), Germany, 6-1, 6-1.
Anabel Medina Garrigues (29), Spain, def. Laura Robson, Britain, 6-2, 6-1.
Nadia Petrova (27), Russia, def. Iveta Benesova, Czech Republic, 6-3, 6-3.
Vania King, United States, def. Galina Voskoboeva, Kazakhstan, 6-4, 6-2.
Chan Yung-jan, Taiwan, def. Kateryna Bondarenko, Ukraine, 6-1, 7-6 (10/8).
Victoria Azarenka (1), Belarus, def. Alberta Brianti, Italy, 6-7 (6/8), 6-4, 6-2.
Jelena Jankovic (19), Serbia, def. Patricia Mayr-Achleitner, Austria, 1-6, 6-1, 7-5.
Li Na (7), China, def. Sorana Cirstea, Romania, 6-2, 6-1.
Zheng Jie (31), China, def. Alize Cornet, France, 6-4, 6-4.
Sesil Karatantcheva, Kazakhstan, def. Timea Babos, Hungary, 6-1, 6-0.
Christina McHale, United States, def. Kiki Bertens, Netherlands, 2-6, 6-4, 6-4.
Petra Martic, Croatia, def. Michaella Krajicek, Netherlands, 6-2, 7-5.
Chanelle Scheepers, South Africa, def. Laura Pous-Tio, Spain, 6-4, 2-6, 6-1.
Olga Govortsova, Belarus, def. Romina Oprandi, Switzerland, 6-4, 6-1.
Bethanie Mattek-Sands, United States, def. Sabine Lisicki (12), Germany, 6-4, 6-3.
Petra Cetkovska (24), Czech Republic, def. Simona Halep, Romania, 6-1, 6-3.
Carla Suarez Navarro, Spain, def. Tamarine Tanasugarn, Thailand, 6-0, 6-3.
Sloane Stephens, United States, def. Ekaterina Makarova, Russia, 6-4, 7-6 (8/6).
Flavia Pennetta (18), Italy, def. Hsieh Su-wei, Taiwan, 6-7 (3/7), 6-4, 6-2.
Varvara Lepchenko, United States, def. Ksenia Pervak, Kazakhstan, 6-2, 6-7 (6/8), 6-4.
Sofia Arvidsson, Sweden, def. Roberta Vinci (17), Italy, 6-2, 4-6, 6-3.
Yaroslava Shvedova, Kazakhstan, def. Mandy Minella, Luxembourg, 6-3, 6-4.
Marion Bartoli (8), France, def. Karolina Pliskova, Czech Republic, 6-3, 6-3.
Agnieszka Radwanska (3), Poland, def. Bojana Jovanovski, Serbia, 6-1, 6-0.
Nina Bratchikova, Russia, def. Monica Niculescu (32), Romania, 0-6, 6-3, 6-3.
Claire Feuerstein, France, def. Vera Dushevina, Russia, 6-4, 6-1.
Stephanie Foretz Gacon, France, def. Barbora Zahlavova Strycova, Czech Republic, 6-3, 7-5.
